The former England international sees defence as the major priority.
The new Black Cats boss has a major task on his hands to turn the club’s fortunes around and Parlour believes he needs to start at the heart of the defence.
“The most important thing he’s got to do is get the right pairing at centre-back,” said the former Gunner.
“I’ve seen (Younes) Kaboul play there and (Sebastian) Coates and they just haven’t got it right at the moment.
“So that’s the first thing he will do, make them more solid… if there’s one man who keep Sunderland up, then they’ve got him,” he added.
Neither of Sunderland’s centre-back recruits have covered themselves in glory this season, and Allardyce will need to quickly identify which two out of his current crop will best serve him going forward.
The former West Ham boss is known for making his teams hard to beat and an injection of steel would be more than welcome in a team that currently holds the worst defensive record in the league - with 18 goals conceded in their first eight games.
John O’Shea will likely form a key part of that defence, given his impressive displays for the Republic of Ireland recently, and finding the man to partner him will be a job Allardyce needs to do sooner rather than later.