Reports in several national newspapers suggested that the 20-year-old was on David Moyes' radar after establishing himself as an integral part of the Blades defence.
Weir has heard nothing, though, but believes it can only be a good thing for his players to be receiving such attention.
"I don't know anything about it, but it is great news for our players to be linked with such big clubs," he said.
"Harry has a lot of attributes, for a young lad he has played a lot of games, and I would not be surprised if clubs were looking at him.
"But we don't want to lose him."