Stewart has caught the eye of several Football League clubs and Posh boss Darren Ferguson will take a close look at the 18-year-old next week after the Irish League season ends on Saturday.
"Jordan is a great kid and still has an awful lot to learn," Glentoran manager Eddie Patterson told the Belfast News Letter. "He goes over to England next week on trial to Peterborough.
"Fingers cross, it will work out for him. He's looking forward to it. We didn't play him at Solitude a few weeks back because he received word that the trial offer was off. His head just wasn't right, so we left him out.
"He's came on from the bench in the past two games against Crusaders and Linfield and made a big impact in both games.
"Jordan is a big player for us. Peterborough have since came back to us and the trial is back on. If he doesn't make it across the water, he's a massive part off my plans as long as I'm in charge. He is a quality kid."
Stewart, who came through the youth ranks at Glentoran, signed a two-and-a-half-year contract extension with the club in November.