Toney has scored 12 times this season already - and The Sun report that Posh have set a price of £13 million.
Posh chairman Darragh MacAntony said: “Toney will break the transfer record for a League One player when he goes. If he goes that. He'll certainly smash the Posh record.
“We don't want to lose anyone in January, but you can't guarantee anything in football.
“If we do lose anyone, they will be replaced."