The 23-year-old has been rumoured to be following former teammate Jordan Henderson to Liverpool.
Manager Bruce told The Journal: "I don't know where that has come from. It's news to me.
"We have been dealing with Liverpool for the past five weeks over the Jordan Henderson deal and there was never a mention that they wanted Lee."
The manager also said his club's pursuit of Wigan's Charles N'Zogbia, a player Bruce signed during his time at the DW Stadium, is over.
"[The transfer] is not going to happen. It has become a bit too rich for us."
Sunderland are currently in Germany on their pre-season tour, where they face Hannover 96 in their next game after drawing 1-1 with Arminia Bielefeld in their opening fixture.