But Fry got the impression The Tractor Boys were not keen on selling to a potential promotion rival.
Simpson (20) made a strong impact during a loan spell at League Two side Swindon Town last season when he scored 11 goals in 30 appearances.
"He’s a young player who will only get better,” Fry said. “I did have a conversation with Ipswich about him, but nothing came from it. I got the impression they didn’t want to let him come to us as a potential rival for promotion.”
Simpson refused to sign the new deal offered to him at Portman Road last season and subsequently handed in a transfer request.
Ipswich, who are the favourites for the 2022-23 League One title, took up their option to extend his contract by a further 12 months at the end of the campaign so they can insist on a fee.
The Hull Daily Mail linked Posh with former Tigers captain Richie Smallwood again this week, although doubts persist about the 31 year-old multiple promotion-winning midfielder’s willingness to move away from the North of England.