Toney is widely expected to leave Posh whether they go up or not at the end of an extended League One campaign.
But Posh, should they unlock access to the riches which accompany a place in the second tier of English football, would rather keep their star man than cash in on a transfer fee that could easily reach £10 million.
Posh director of football Barry Fry said: “It’s accepted we have no chance of keeping Ivan if we don’t get promoted this season.
“And that’s fair enough. Ivan has been here for two seasons. He scored 23 goals last season and if we ever start playing again he will probably get more than 30 goals this season.
“He’s served us well and it’s the best £400k or so we’ve ever spent.
“But we’d rather keep him than sell so if we do go up I have no doubt we will offer him the biggest contract Peterborough United have ever offered.
“And you never know he might fancy staying with us and playing every week rather than take a chance on a bigger club so it would be unforgivable if we didn’t make every effort to try and keep him.
“He’s sure to get some big money offers, but Ivan is a humble, lovely lad and he won’t make a move purely for money in my opinion.
“We’ve turned down some big bids in the past for him and he’s been fine with that.
“He’s kept working hard and playing with total commitment and he’s turned into a tremendous all-round footballer.
“It’s important to remember Ivan is not just an exceptional goal-scoring forward, he’s also an outstanding defender.
“We’ve sold some top class strikers in our past, but none have been able to defend anywhere near as well as Ivan.”
Posh turned down bids n excess of £4 million for Toney last August when his suitors were believed to include Championship club Charlton Athletic.
Premier League teams Burnley and Bournemouth were reportedly interested in Toney in January - Toney scored against Burnley in the FA Cup - but Championship promotion contenders Brentford were the most persistent bidders.
Burnley claim to have been quoted a transfer fee of £13 million!
Posh signed Toney from Newcastle United in August, 2018.