Posh have already turned down two bids from from promotion-chasing Championship side Bournemouth, believed to be of £1 million and £1.5 million.
Posh are believed to be holding out for more than double the higher amount as they believe Dembele is worth more to the club by helping them stay up before leaving on a free transfer when his contract expires in June.
The transfer window closes at midnight on Monday (January 31). Dembele missed Tuesday’s draw at Birmingham because of injury and he’s a doubt for Saturday’s game at home to Sheffield United (January 29).
“There is no way we will sell him on transfer deadline day,” Posh director of football Barry Fry said earlier this week. “Because that would give us no time to sign a replacement.”
Fry couldn’t be reached for comment today (January 27).