The 24-year-old, released by Port Vale last month following a fall-out with the club, was subject to a six-figure bid in the January transfer window.
Vale rejected the enquiry but, with Burge now a free agent, he would welcome a renewed approach.
"I have had a lot of interest," he told Press Association Sport. "In January time there was Peterborough that were pretty keen on taking me, so now I am out of contract there is no fee it makes it a lot more appealing to a club.
"That was in January, but Peterborough are obviously a massive club. It's disappointing that they have come down but I am sure they will bounce back up."
Despite hinting at a move to Posh, Burge feels he is capable of playing in the Championship and is keen to prove people wrong.
"I am confident I could do a job at Championship level," he added. "It's a lot easier to go into the Championship level when you have had more experience.
"I have obviously had games and won a promotion so now I am in a better position to make that step up."
- Sports & Recreation