Wright, who will soon be out of contract at The Valley, helped the Gills to promotion via Saturday's play-off final.
With the Addicks having been relegated and Gillingham bouncing back from the basement division, the 19-year-old could well find himself playing League One football next term.
"It looks like that way, but we'll just have to wait and see where that is," he said.
"I came to Gillingham looking to play games and there's nothing better than this. The boys are a great bunch of lads and I've really enjoyed my time at the club."