Former Hull City defender Turner has been linked with a possible move to Bolton with Owen Coyle looking to bolster his defensive options.
Turner was missing from the Sunderland side that won 2-1 at Kilmarnock on Wednesday to fuel speculation over his future, but Bruce insists there was nothing sinister in the defender's absence.
Bruce admits he is looking to offload the likes of Matt Kilgallon, George McCartney and Nyron Nosworthy, but he insists he has no plans to lose Turner.
"There are players we'd like to move on, but Michael definitely does not fall into that category," Bruce told the Northern Echo.
"I think we all know who I'm talking about - Nyron Nosworthy, Matt Kilgallon and George McCartney all need to go and play somewhere.
"They're the ones who we'll look to move on, but none of my first-team squad and certainly not Michael Turner. I want all of our big players to stay.
"The thing about Michael is that he's a big lad and he's been out for a long time. It's fair to say that he still needs more games, but he's coming back from a serious knee injury and it's important that we don't rush him."