The Portuguese coach, who was linked heavily with the Liverpool job prior to Arne Slot’s appointment, has also been mooted as a potential replacement for Pep Guardiola should he leave Manchester City at the end of the season.
The 39-year-old is seen as a progressive and modern coach and has won the league with Sporting on two occasions since joining in 2020. His side have won all nine league games this season, too, and currently sit six points clear of Porto at the top of the table.
United would have to pay a €10million (£8.3m) release clause to prise him away from the Portuguese club but Amorim is said to be willing to take up the role.
Earlier in the day, Amorim refused to comment on any speculation linking him with a move to Old Trafford and insisted he was happy to continue with his current role at Sporting.
‘I was expecting that question and obviously I’m not going to talk about the future, because otherwise I’ll always have to comment, so it’s not worth it, I won’t comment,’ he told reporters.
‘I’m very proud to be the coach of Sporting, that’s all.’
Pressed further about a potential meeting with United and reports crediting the Red Devils with a move for Sporting youngster Geovany Quenda, Amorim added: ‘I didn’t know about United’s interest, if there is any.
‘Quenda is still very young, has few games and it’s good that he keeps his feet on the ground. The price is not up to me, it’s up to the president. I won’t comment on my future.’
Amorim already has fans within the current United team, with fellow countryman Bruno Fernandes full of praise for the 39-year-old and tipping him for a successful career in management.
‘They have been consistent, the signings have been right and they are in a very good moment. It’s a very well-prepared team,’ the United skipper said on international duty last month when asked about Amorim.
‘Coaching Sporting and winning championships is not easy, Sporting went 20 years without winning championships and Amorim arrived and has already won two. This shows that the work has been done well.”
‘If he could manage to do the same in England, Spain or anywhere else, you will never know until you get there, but I am sure his qualities are there for everyone to see.’
Other managers, including Gareth Southgate, Thomas Frank and Xavi, have been heavily linked with the vacant post.