The Black Cats had a joint bid amounting to more than £12million accepted for Darron Gibson, Wes Brown and John O'Shea several weeks ago, but have not yet managed to push through a move for any of them.
Now with competitors lining up to challenge Bruce in the race to capture the three, he is hoping to make a breakthrough after a whirlwind of transfer activity on Wearside last week.
Republic of Ireland international O'Shea seemed the most unlikely of the trio to end up at the Stadium of Light, and although there have been positive noises on that front in recent days, Arsenal and Stoke have also been linked with him.
The Potters, as well as Everton, have been touted as possible purchasers for fellow defender Brown, while midfielder Gibson's name is also on Newcastle boss Alan Pardew's list.
Sunderland are due to start pre-season training on Wednesday, and there will already be a series of new faces in attendance with Connor Wickham, Ji Dong-won, Craig Gardner, Keiren Westwood and Sebastian Larsson having joined the club, while Ahmed Elmohamady's loan move has become permanent.
But Bruce is determined to make a big push this season and his shopping mission is not yet over.
He could yet be in the market for another striker - he currently only has Asamoah Gyan, Wickham and Ji on the books - although sources on Wearside today played down reports linking the club with Stuttgart's Russian frontman Pavel Pogrebnyak.
But following the return of loan signings Nedum Onuoha and John Mensah to their respective clubs, defence is now a priority, and that is why he is hoping to make progress on O'Shea and Brown.