Reports last week suggested Ipswich Town, the current favourites for the 2022-23 League One title, were keen on signing Taylor.
But Posh director of football Barry Fry insists his club want to add a couple of midfielders to their squad rather than let any more of them leave. Kyle Barker and Serhat Tasdemir were released by Posh at the end of last season, while Jorge Grant and Idris Kanu have been made available for transfer.
Taylor (23) is seen as a key player for a Posh promotion push from League One. He and Jeando Fuchs are currently the only two fit central midfielders at the club as Oliver Norburn will be absent with knee ligament damage until Christmas, but Fry has dismissed a link with Plymouth midfielder Panutche Camara
Fry, who will join a Posh recruitment and planning party in Las Vegas on Wednesday, said: “I’ve had no contact from Ipswich for any of our players. In fact I’ve had no contact from any club about anyone. It’s far too early in the summer for that. There are still games going on.
"I will say we have no interest in selling Jack Taylor. If someone offered £10million we might, but that isn’t going to happen. We are looking to recruit a couple of midfielders so I doubt we will let anyone go from that position.
"These are all things that will doubtless be discussed in Vegas.”
Pym spent the second-half of last season on loan at League Two strugglers Stevenage, but they would struggle to match the keeper’s wage demands.
Broom spent last season on loan at League One Plymouth Argyle. They want the 25 year-old, but have yet to come up with an offer.