The Telegraph says Amorim, who won 14 caps for Portugal as a player, is part of the new generation of coaches that have put themselves on the map at a young age.
The Sporting boss is just 36 but has already worked previously with Braga.
At Braga he won the Portuguese Cup within months of taking over, which saw Sporting pay €10m to secure his services - the third highest fee for a manager in history.
With Sporting, Amorim won the Portuguese Cup once again, beating Braga in the final, and has also led them to the league title.
Those exploits have attracted the attention of those making the key decisions on the red half of Manchester.
Amorim did recently sign an extended deal, which included a hefty buy-out clause, which will no doubt come into consideration.
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