Scott Mills was questioned in 2018 over historic allegations of serious sexual offences against a teenage boy but the case was later closed due to lack of evidence.
The Metropolitan Police said a man, who was in his 40s at the time of the interview, was investigated over allegations reported to have happened between 1997 and 2000.
As first reported by the Mirror, the case was dropped in 2019 after the CPS deemed there was insufficient evidence to bring charges.
On Monday, it was announced Mills had been sacked by the BBC over allegations related to his personal conduct. The BBC have not given any further details over the allegations and it is not clear what, if any, role the police investigation played in his sacking.
The BBC has been approached for comment about the police investigation.
