Bruce has been credited with an interest in West Ham's Robert Green in recent weeks, while there have also been suggestions that Portsmouth's David James has been under consideration.
Confirmation that Craig Gordon is likely to be out until February with a broken arm means the speculation has resurfaced as the January transfer window approaches.
But Fulop, looking ahead to his first start since the end of August against Arsenal this Saturday, feels Bruce already has the goalkeepers at his disposal to save the club some money.
I don't think the manager needs to bring in a new goalkeeper,
insisted Fulop. Sunderland has three good goalkeepers I include Trevor Carson as well. Craig is Scotland's number one and a very good goalkeeper and I am an international as well.
But that is what the manager is paid to do make decisions like that, sign and sell players. But all three of us want to prove to him that there is no need to sign another goalkeeper.
While Gordon, the club's £9m signing, has been showing the sort of form that made him such a big prospect a few years ago with Hearts, both Fulop and 21-year-old Carson have signed new deals this year.
The competition means two of the three goalkeepers are left frustrated while the other stands between the posts in the Premier League.
Now, following Gordon's recent blow after a clash with Tottenham's Jermain Defoe, Fulop is ready to take his latest chance.
The 26-year-old started the season in goal but was forced to spend time on the sidelines after finally accepting that a worsening heel injury needed treatment.
It's not nice. You're here to play. As a foreign player playing here you miss your family but if you're playing it doesn't hurt quite so much, said the Hungarian.
In football, you should be looking to play. I have never been someone who is willing to sit on the bench and pick up my wage.
That would be easy money but I've always wanted to work hard and to prove to my family, my friends and my teammates that I'm a good goalkeeper. I think in the longterm, that attitude brings you rewards. You will get what you deserve. It also means that I'm in a good condition to play now.
Gordon's impressive form prior to his injury blow at White Hart Lane 11 days ago made him an automatic choice. Now, though, Fulop is determined to make the most of his team-mate's misfortune.
I don't think the manager has decided yet who his number one is, said Fulop. The more games you get the more chances you get to impress and I hope we get a good result against Arsenal now.
It was the last pre-season game, I did my heel. It was a bad injury and the first three games I played with injections.
You can't do that forever and there was a time to say I need a rest'. It took five or six weeks to heal properly and in that time Craig came in and did fine.
It was no question of the manager changing a winning team and a keeper playing well. Injuries are a different question and now I hope I can step in and do what I did last season which is play well.
The visit of Arsenal will also represent a further opportunity for Darren Bent to prove he can score goals against the best defenders around after failing to find the net for England last weekend.
Bent's form in front of goal this season led to his international recall and his scoring record will determine whether or not he is retained when Fabio Capello announces his next squad in March.
Yesterday, however, the £10.5m man learned that he has not had another goal added to his season's tally.
The Premier League's dubious goals committee ruled that Sunderland's final strike in the 5-2 win over Wolves in September must be credited to defender Michael Mancienne.
Bent's shot deflected off Mancienne and it means that the Sunderland striker remains on eight rather than the nine that would have had him level with Didier Drogba and one behind Fernando Torres.