New Reds manager Roy Hodgson is said to be an admirer of the England Under-21 international and has been linked with a move for the former Middlesbrough and Wigan midfield enforcer.
Bruce however insists he knows nothing of any Reds interest and with Lorik Cana having left Wearside this summer, the Sunderland manager is unlikely to allow Cattermole to depart as well.
When asked about Cattermole after his side's friendly win over Munster XI, Bruce said: "I don't know anything about that, and I have absolutely no intention of letting Lee leave this club - none whatsoever."
Bruce is also keeping his fingers crossed after young striker Martyn Waghorn was stretchered off in Ireland.
The 20-year-old, who spent last season on loan at Leicester, damaged a knee after scoring twice at Thomond park in Limerick as the Black Cats opened their pre-season campaign with a 2-1 win.
Bruce is hoping an initial assessment, which suggested that the injury is not serious, will prove accurate.
He said: "Waghorn is a concern because of the way he landed on his knee.
"We hope he hasn't done anything serious - that's the biggest fear.
"We will study the evidence and have a look at it, but touch wood, we are thinking at the moment that he will be okay."