The Scottish Sun made the claim with Brentford the club believed to have made an acceptable offer for the 24 year-old who scored 26 goals in a shortened campaign last season.
The Peterborough Telegraph reached out to Posh officials this weekend, but they declined to comment.
Posh are believed to want £10 million for Toney. Brighton, Celtic and Rangers are other clubs to have been linked with a move for a striker signed for around £300k from Newcastle two years ago.
Posh are prepared to keep the player if a suitable fee isn’t forthcoming.