The 34-year-old, who joined the League One outfit on a short-term deal last month, has impressed for the club in their recent upturn in form.
"When the campaign is over we'll sit down and assess the situation. I'm sure Barry will tell us his views then," Wilson told The Star.
"Personally, I'd love to keep him whatever division we are in because Barry has got the ability to be an influence in the Championship.
"I don't know his circumstances and I'm sure, with how well he's doing, he'll have plenty of options. But the fact that he came here, that he decided to choose us in the first place, was a real feather in our cap."
United currently sit top of League One.