AS says the Hammers are showing interest.
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What is Sörloth's own attitude towards the future is not yet clear.
The Norway striker has a contract with Villarreal that runs until the summer of 2028 and a mooted buyout clause of €40m.
West Ham have also been linked with attacking targets Youssef En-Nesyri (Sevilla) and Georges Mikautadze (FC Metz) this summer.