The 17-year-old - who stands at 6ft 2in tall - is still waiting to make his senior debut for the Australian giants, but he has been in and around the first team over the past year.
Cook was on the bench for an Australian Cup qualifying loss to Macarthur last year, while also making the matchday squad for the final two rounds of the 2023-24 A-League season.
A report from The Sun claimed that Championship outfit Sunderland were poised to bring Cook to the UK, and there would be no hold-ups thanks to his British passport.
Cook is reportedly desperate to prove himself in England - where his father hails from - and the Black Cats were apparently prepared to offload Nathan Bishop in order to make room for the A-League prospect.
Man United scouts 'impressed' by Cook
However, a separate report from journalist Alan Nixon claims that Man United are now attempting to hijack Sunderland's move for the 2007-born starlet, whom their scouts have taken a serious liking to.
While the pathway to the first team may be clearer for Cook at the Stadium of Light, the report adds that the pull of the Premier League could be enough to convince him to snub a move to Sunderland.
Man United have already poached one talented prospect from Perth Glory's academy ranks this summer, concluding a deal for 17-year-old James Overy at the beginning of the window.
Overy joined up with the Red Devils' Under-18 squad, and Cook would be expected to follow the same path with a view to first-team progression in the future.
What is the latest on Man United's goalkeeping situation?
As Erik ten Hag prepares for a third year in the Man United dugout, the Dutchman is still working with Andre Onana as his undisputed number one, in spite of some shaky displays in his debut campaign.
Ten Hag's faith in Onana restricted fellow debutant Altay Bayindir to just one appearance for the Red Devils in the 2023-24 season, and the Turkey international is already being linked with a move back to his homeland.
Should Bayindir indeed depart in the coming weeks, Man United have apparently taken a liking to Christos Mandas of Lazio, although Manchester City are also keeping an eye on his situation.
Meanwhile, third-choice shot-stopper Tom Heaton has extended his contract at Old Trafford for another season, while 20-year-old Radek Vitek might enjoy more first-team exposure next season too.