Wilson is a free agent after leaving Bristol City earlier this summer and he is training with United to keep fit.
United boss Jackie McNamara has refused to rule out a move for Wilson and he will cast an eye over him in training.
"Mark was my replacement at Celtic so it shows I don't hold a grudge," said McNamara in the Daily Record.
"He's in training with us to keep himself fit. You never know what might happen. He's a good player with good experience."
The 29-year-old admits he would be interested in a move back to Scotland to rejoin former club United.
"My family are still down in Bristol but I'm up in Scotland this week so was looking for a bit of training. I'm grateful to them," said Wilson.
"I would favour coming back up the road as things didn't really work out down south. Our home is still up here so I'd like something back in Scotland.
"Right now there's nothing on the table but I wouldn't rule anything out. If United offered me something I'd definitely consider it. The club is always in my heart because I had some of the best times of my life here."