Turner, 27, has been missing since November 22 after he damaged his knee when colliding with a post as he cleared an effort from Everton's Tim Cahill off the line at the Stadium of Light.
Turner visited a specialist last week after complaining of pain in the knee following his return to training amid fears that he had suffered a setback.
He was given the all-clear to step up his recovery, but rumours have been circulating that his season could be over.
However, Bruce preferred to take a more optimistic view of Turner's chances, insisting that the former Hill centre-back could be back much sooner.
"We have seen a specialist and the one thing he's got to do now is get his thigh muscles stronger," Turner told Sunderland's official website. "It's still disappointing for Michael, but we are still hoping he will be back some time in the coming weeks.''
Turner has been conspicuous by his absence in recent weeks as a defence which for so long this season had proved resilient has been less than effective.
Of the 15 games the Wearsiders have played in his absence, they have won only five, conceding 22 goals in the process.
Indeed, they have shipped 11 of those in their last four Premier League outings, all of which have ended in defeat, to severely dent their hopes of securing a top-six finish.
Sunderland face Arsenal at the Emirates Stadium on Saturday before Liverpool head for Wearside, and they then travel to big-spending Manchester City after the break for international matches as a tough run of fixtures eventually draws to a close.
Bolo Zenden is the latest man to join Bruce's casualty list, he will miss Sunderland's trip to Arsenal on Saturday with a calf strain.
However, Bruce is hoping that the 34-year-old Dutchman will be fit for Liverpool's visit to the Stadium of Light on March 20 with the club's exit from the FA Cup meaning they have no fixture during the previous weekend.