According to journalist David Ornstein, the 39-year-old is open to accepting the switch immediately, and the two clubs are in discussions, with Man United moving quickly after sacking Ten Hag as manager on Monday.
Amorim has 'verbally agreed' to become Man United's next boss, according to journalist Ben Jacobs, and it is possible that there could be an announcement in the near future confirming his arrival in Manchester.
Here, Sports Mole looks at how the 20-time English champions could line up under Amorim, should the Portuguese be confirmed as Ten Hag's permanent replacement at Old Trafford.
Amorim has largely played a flexible 3-4-3 system at Sporting, so it is fair to assume that he would be looking to bring that to Man United, which would be a complete shift for the team.
Andre Onana's spot between the sticks is not in doubt; the Cameroonian has been much-improved after a shaky first season at Old Trafford, and with Amorim liking his goalkeeper to take a big role in the build-up, Onana fits the brief.
Leny Yoro is yet to make his competitive debut for Man United, having fractured his foot during pre-season, but the Frenchman is expected to be back in December, and the generational talent has the potential to transform Man United's defence.
Matthijs de Ligt and Lisandro Martinez would also be starters under Amorim, with Diogo Dalot as the right-sided wing-back, while Luke Shaw, providing that he is able to overcome a calf issue in the near future, is perfect for the left-sided wing-back role.
Amorim's style has worked well in Portugal, but it remains to be seen whether it can be successful in the Premier League.
Manuel Ugarte has been underused this season, with the Uruguay international bizarrely dropped for the West Ham United clash after putting in an outstanding performance against Fenerbahce in the Europa League, and he would surely be a key player under Amorim, as his style and system requires a ball-winning midfielder.
Kobbie Mainoo is currently on the sidelines through injury, but he should be back over the next two or three weeks, and there will undoubtedly be a role for the outstanding young talent in the XI.
The front three is where it gets interesting; Rasmus Hojlund should be the centre-forward, as Joshua Zirkzee has struggled to impress this season, while Alejandro Garnacho has been Man United's biggest attacking threat, and there simply has to be a spot in the XI for the Argentina international, most likely down the left.
That only leaves one position and two players fighting for it, with Marcus Rashford and Bruno Fernandes yet to be named in this piece.
It is incredibly difficult to imagine Fernandes being dropped even considering his inconsistent form this season, as he is a reliable contributor of goals and assists, and he is capable of thriving down the right, providing that he has the licence to drift into the middle and is not asked to operate in a wide area.
Amorim's arrival would not end Rashford's career, far from it, as the England international could certainly find himself in the XI on a consistent basis if he is able to show his best form once again.
Amorim generally looks for his side to flood the penalty box when attacking, so Garnacho, Hojlund, Fernandes and Mainoo could be the most advanced of the 10 outfield players, while Garnacho and Fernandes would be asked to come inside to open up space for the wing-backs, with Dalot in particular better going forward then he is defensively.