BUFFALO, N.Y. — The clock is ticking on Alex Tuch and the Buffalo Sabres.After the Sabres were eliminated in the second round of the NHL playoffs with an overtime loss to the Montreal Canadiens on Monday, Tuch and the Sabres have until July 1 to agree on a new contract before the 30-year-old winger hits the open market.Speaking to reporters after his exit meeting with general manager Jarmo Kekäläinen and coach Lindy Ruff, Tuch still didn’t have a lot of clarity on his contract situation, which has been hanging over him all season. He said Kekäläinen expressed that the Sabres would like him back. And just like this time last season, Tuch said he has loved his time in Buffalo. But none of that guarantees the two sides will be able to agree on a contract that makes sense.“I have no idea,” Tuch said. “I wish I could tell you the future, honestly. I really just don’t know how it’s gonna unfold. It’s something that I’m going to have to do a lot of thinking about.“I mean, I love it here. I’ve loved my time here. I’ve loved playing hockey here. I’m going to do whatever’s best for myself and my family. That’s all. That’s my power and consideration. Like I said, I don’t know how talks are going to proceed. I don’t know what they’re going to say, I don’t know the future. But my main priority is my family and where we’ll be, where my kids will grow up, and who we surround my kids with. There’s a lot of aspects that go into it. It’s not just numbers, it’s not just where to play. There’s endless amounts of possibilities and options for a guy going into free agency. You don’t really know anything until everything’s laid out in front of you. So, I’m going to take some time in the next few weeks to really figure it out and see how it goes.”Tuch turned 30 during the Montreal series. Under the collective bargaining agreement, the Sabres are the only team that can offer him an eight-year contract, but that’s a term that comes with some risk given his age. The one comparable that stands out is Los Angeles Kings forward Adrian Kempe, who signed an eight-year contract extension worth $10.625 million per year at the beginning of the season. But the Sabres might point to the contract Nick Schmaltz signed in Utah, which was eight years and $8 million per year.What’s clear in hearing Tuch talk is that the decision isn’t going to be solely about money. He grew up two hours east of Buffalo and was a fan of the Sabres. He has spent five seasons with the organization and finally helped get them back to the playoffs.He and his wife, Kylie, have two sons under 3 years old and built a house in a suburb of Buffalo. They are expecting their third child later this year. Tuch said his oldest son, Tripp, who turns 3 in December, has become obsessed with hockey. He has a mini rink in his playroom that he plays on in in-line skates. He has his dad introduce him as No. 89 for the Buffalo Sabres and play “Money for Nothing” by Dire Straits so he can be just like his dad.Those types of things will be weighing on Tuch as he decides what to do next. Tage Thompson, who lives across the street from Tuch, expressed right after the Game 7 loss how important it would be to have Tuch back, and he echoed that in his interview on locker cleanout day.“I don’t think it’s a secret that everyone in that room wants him to come back,” Thompson said. “He’s a huge piece of this team, a massive reason why we got to where we did.”Tuch has played at least 74 games in each of the last four seasons and has at least 59 points in all of those seasons. He had 66 points in the regular season this year before putting up 7 points in Buffalo’s six-game first-round series against the Boston Bruins. But the last image of Tuch this season wasn’t his best. He had zero points and was minus-eight in the Sabres’ seven-game series against the Canadiens.“I thought my work ethic was there as the series went on,” Tuch said. “I thought my attention to detail got better. I thought it slipped away from me a little bit in the middle of the series there, some frustration sank in, which for me is a little uncharacteristic because I pride myself on being a pretty consistent player. So offensively, I felt like I let my teammates down with that, but at the same time, I was really proud of my effort.”Kekäläinen remained steadfast in his message that he values Tuch, but it’s clear he’s also going to make sure the price is right.“He’s been an important part of our success,” Kekäläinen said. “He’s always giving some of the most ice time of any of the forwards, killing penalties, playing power play; he’s a consistent goal scorer. He’s a valuable part of our team. Just like I’ve told him, and I tell everybody in the same situation, we make our decision based on, ‘How can we make our team better?’ And we have to come to an agreement that this is the type of contract that we can still make our team better. And hopefully we can do that.”Tuch is arguably the top free-agent forward available on the market, so it’s hard for the Sabres to become better in the short term by letting him walk. But they do have young players ready to step into bigger roles. Zach Benson and Josh Doan are already looking like core players for the Sabres. Konsta Helenius, Noah Östlund and Jiri Kulich are in the mix for top-nine roles next season, too. The Sabres have $12.9 million in salary-cap space with Tuch and Beck Malenstyn as key unrestricted free agents and Benson, Peyton Krebs and Michael Kesselring as notable restricted free agents. They can free up some room by finding a way to move on from Jordan Greenway’s $4 million, but other tough decisions could be coming if they want to fit Tuch’s salary.Quick hits1. Thompson said he was dealing with lower-back issues during the playoffs, but nothing that was too much. He attributed it to the wear and tear from a long season that included playing for Team USA at the Olympics. Owen Power was playing through a Grade 3 ankle sprain late in the Montreal series. Defenseman Logan Stanley was also out of the lineup because of an injury, and Sam Carrick tried to return too quickly from his injury. Otherwise, the Sabres didn’t reveal any other significant injuries, but Kekäläinen did say quite a few players were battling through something.2. Kekäläinen mentioned he told Benson and defenseman Bo Byram he was hopeful to sign them long-term. Benson, 21, is a restricted free agent, and Kekäläinen raved about the season he had, calling him a “core piece.” And Kekäläinen thinks Buffalo’s top four on defense is a critical component to the team’s success. Byram is a big part of that and is eligible for an extension July 1.“I think there’s a ton of things, first and foremostly being that I don’t want to lose anymore,” Byram said when asked what he’ll think about when considering whether to sign long-term. “I want to be on a good team every year, and I want to compete for a Stanley Cup every year. I want to be playing important games every year. And then there’s more personal stuff: where you fit in, what your goal is, whatever. A ton of things that go into it.”3. The Sabres signed Lindy Ruff to a two-year extension Wednesday, and Kekäläinen said it was a “no-brainer.” Ruff didn’t outright confirm his staff would be back intact, but he praised the work they did this season and said he puts a high value on continuity. Kekäläinen alluded to some more changes in the front office that could be announced in the coming days.