The 27-year-old midfielder is currently is Edinburgh for talks to see whether he can agree a deal.
The summer signing has attracted interest from a Championship and a League One club and has a buy-out clause in his contract but a representative from the club has told the Peterborough Telegraph that the offer that has been accepted is “nowhere near that.”
Grant arrived in the summer from Lincoln after Posh triggered a release clause in his Imps contract. He had helped Michael Appleton's side to the League One Play-off final but he struggled to make an impact in the Championship.
He appeared 26 times (21 starts) in the Championship last season but started just one of the last 20 league matches of the season; away at Fulham on February 23.
He did start against Manchester City in the FA Cup in March, his only start under Grant McCann.
Speaking earlier this month Posh Director of Football Barry Fry said: "We got Jorge on the cheap considering how good he had been at Lincoln.”
“He also has a release clause in his Posh contract in the event of relegation from the Championship, but I doubt anyone would reach it.
"He did struggle last season and it’s difficult to see him fitting into the manager’s style of play, but we do want a fee for him. We want to move him on, but if he stays he was at least very good the last time he played in League One.”