The former Cheltenham Town and Bristol City striker struggled for regular football this season and has now been deemed surplus to requirements by Posh following their promotion to the Championship.
Sunderland were keen on Eisa in the summer of 2018 following their relegation to League One, but he eventually joined Bristol City – teaming-up with Lee Johnson at Ashton Gate.
But having made just six appearances at Ashton Gate, the Sudanese striker joined Peterborough in 2019.
His first season with the side was a success as he netted 16 times in 35 games before the campaign was curtailed.
However, Eisa found himself behind Jonson Clarke-Harris and Siriki Dembele in the pecking order at London Road this year and is now one of four players to be transfer-listed by Darren Ferguson.
The Peterborough boss told the club's website: "Mo needs to play regularly.
"He is too good a player not to be and he may find it difficult as he did this season to be in our starting line-up.
“He is a great lad and played a massive part.”
Posh president Darragh MacAnthony believes that Eisa could help lead a side to promotion from League One next season – but has warned that a deal will not be done on the cheap.
"Guaranteed 25 league goals in 45 starts thats for sure,” he tweeted.
"But wont be cheap of course. Would drive a promotion campaign for a good L1 club.”