The Sporting CP manager is a hot property as the end of the club season approaches.
Per The Mirror, the Hammers are hoping to steal a march on other top clubs to secure Amorim.
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The Portuguese is interested in the position, as he would get to showcase his talents in the Premier League.
He is said to have been accompanied for the talks in the UK by businessman Raul Costa.
The two were photographed boarding a plane together, with Amorim away from Sporting for the next two days.