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.
Wanted: Wes Brown
Wanted: John O'Shea
Wanted: Darron Gibson
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.
Following the return of loan signings Nedum Onuoha and John Mensah to their respective clubs, defenceis now a priority, and that is why Bruce is hoping to make progress on O'Shea and Brown.
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.
Captured: Steve Bruce has brought in Connor Wickham (left) and Craig Gardner (right)
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 played down reports linking the club with Stuttgart's Russian frontman Pavel Pogrebnyak.
His agent confirmed there is interest from the Premier League amid reports Sunderland were intalks to sign the Stuttgart striker.
The Russia international has spent the past two seasons with Stuttgart and has reportedly been wanted by Liverpool and Tottenham in the past.
Linked: Pavel Pogrebnyak (centre) is rumoured to be interested in a move to England
Reports in Germany over the weekend claimed Sunderland are keen to sign the 27-year-old and the forward's agent Oleg Artemov acknowledged there is interest from England.
'For now, I can not tell you anything,' Artemov told Sports.ru in relation to the Sunderland link. 'Let's leave this piece of news without any comments.
'There really are some offers for Pogrebnyak, but today it's all still at the negotiation stage.
'The interest from German and English clubs still exists. However, we haven't received any new offers.'
The holiday is over, chaps! Premier League stars back in training ahead of new seasonReading demand ?10m for Long as Everton, Sunderland and Toon circleCeltic hoping to beat Sunderland and West Ham to out-of-favour striker BellamyAll the latest Sunderland news, features and opinion
Explore more:People: Steve Bruce, Pavel Pogrebnyak, Craig Gardner, Sebastian Larsson, Wes Brown Places: Liverpool, Newcastle, Republic of Ireland, Germany, United Kingdom, Russia