Payne impressed during the second half of the season after arriving at London Road on loan in January.
The 21-year-old is still under contract at Gillingham, who will play in League One next season along with Posh.
Ferguson told the Peterborough Telegraph: "I will try and sort something out with Jack and Gillingham but it's up to Gillingham, who I don't think have sorted their retained list yet.
"To be honest, apart from Jack, I'm not really bothered about signing anyone else. He is an exceptional footballer who suits the way I like to play."
- Sports & Recreation