McCourt, a Posh transfer target in the past, is a free agent after he was released by the Scottish champions at the end of last season.
The 29-year-old linked up with Darren Ferguson's side this week and is expected to play a part in Peterborough's friendly at Northampton on Saturday.
"We have had the white Pele, now the Derry Pele is in for us to have a look at. Funny I tried signing him before he went to Celtic," Posh chairman Darragh MacAnthony told his followers on Twitter.
McCourt, capped 13 times by Northern Ireland, has been linked with Sky Bet Championship club Birmingham and Major League Soccer outfit San Jose Earthquakes.