Rangnick will have a say in who succeeds him in the Old Trafford dugout, and a number of names - including Mauricio Pochettino, Erik ten Hag, Brendan Rodgers and Zinedine Zidane - have been linked with the post.
Yahoo! Brasil claims that Amorim is also on Man United's shortlist of potential candidates, having impressed during his time in charge of Sporting Lisbon so far.
The 36-year-old only took over at Sporting in March 2020, but in his first full season at the helm he led the club to their first Primeira Liga title for 19 years.
Sporting also won the Taca da Liga in a double-winning campaign, with Amorim retaining that trophy, having also won it with Braga the season before.
However, the former Portugal international is understood to have a £25m release clause in his contract at the Estadio Jose Alvalade, making him an expensive option for Man United.
Pochettino is still thought to be the front-runner for the job, following reports that he is open to leaving Paris Saint-Germain. body check tags ::