HITC Sport understands that the Posh are leading the race for the former Tottenham Hotspur prospect.
Crewe Alexandra and rivals Port Vale had been leading the chase for the former Tottenham Hotspur prospect, who has set his sights on a move back to England to kick-start his career.
Once regarded as one of the best young players in world football, Coulibaly signed for Spurs in a blaze of glory but he never made the breakthrough at White Hart Lane and moved back to Italy where his footballing career had begun.
But now Coulibaly wants to re-ignite things and has already snubbed a host of Premier League and Championship clubs as he does not want to spend any more time playing in youth or reserve teams, which is why he has targeted a League One or Two side.
He has been training with Crewe, but now Peterborough have stepped in and it is believed Coulibaly is tempted by a move to London Road, given their record of developing young talent.
Coulibaly linked up with the Posh earlier this week and has even taken part in a trial game, and HITC Sport understands that Peterborough's director of football Barry Fry has opened talks regarding a permanent deal for the young Ivorian.