The 24-year-old impressed during what was a devastating season for West Ham, scoring seven goals and providing three assists in his 34 games.
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As a result, some of the Premier League’s biggest sides are keen on adding the former Leeds man to their squad.
According to Teamtalk, Man United have entered the race alongside Tottenham as they seek to add a first-team ready left winger.
West Ham are demanding a fee of around £50 million for Summerville, with the forward contracted until 2029.
Due to the club’s financial situation following relegation, however, they may be open to negotiations.