The Blades are the front-runners with them being a top-flight club as Wilkshire's displays in Germany impressed former coach Guus Hiddink, who was surprised at the fact the player was not with a Premiership club.
"He doesn't know his own possibilities because he is a modest player, too modest," Hiddink told the Bristol Evening Post.
"But when you see him playing (against Italy), he wasn't a star player but doing a very good job."
The 24-year-old joined the Robins from Middlesbrough in 2003 for £250k and made 103 appearances for City.