Robson last month signed a short-term deal with the Blades after leaving MLS side Vancouver Whitecaps.
The 34-year-old Scotland international has been an instrumental figure in a run of form which has propelled Wilson's side to the top of the League One standings, and the Blades boss is planning talks with the former Middlesbrough and Celtic playmaker to persuade him to stay in South Yorkshire.
"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."