Bruce is facing the heat from the Newcastle fans after a poor start to the season that has seen them lose three of their opening four Premier League games.
They only have a point on the board and the Newcastle manager has been audibly jeered by fans both home and away at the start of the campaign.
More damaging claims have been made this season with suggestions that Bruce clashed with players after the Manchester United defeat and first-team coach Graeme Jones had a bust-up with Dwight Gayle.
Parlour stressed that the claims are not helping Bruce and the situation Newcastle are in, but conceded that it is natural that he is under pressure at St. James’ Park as results have not been good enough.
He feels Newcastle’s lack of resources will save Bruce from the sack as no other manager is likely to agree to work under such financial constraints.
Parlour said on talkSPORT: “Reports like this do not help, saying that he had a bust-up with him and that shouldn’t be in the papers, to be honest.
“You are on the back foot straight away as a manager if you are getting reports that players are falling out with coaches and it doesn’t help the situation they are in.
“But it is all about results and if they beat Leeds tonight then suddenly he is in the good books and that’s what every manager is feeling.
“Most managers are exactly the same, you look across the board. If you get a couple of bad results, every single manager is under pressure.
“But they know exactly the situation they are in as a manager and realistically if you don’t get results you get sacked.
“I don’t think Mike Ashley is going to get a better man than Steve Bruce with the resources he has got at the moment.
“And that’s why probably at the moment he won’t get sacked because he is doing the best he can.”
The Newcastle manager will hope to get some relief with a result against Leeds tonight at St. James’ Park.