The Premier League club has been linked with numerous players this summer as technical director Tim Steidten tries to strengthen Julen Lopetegui’s squad.
However, Summerville - last season’s Championship Player of the Year - has emerged as the London club's primary target.
Sources say talks are at an advanced stage and personal terms with the 22-year-old are not expected to be a problem.
Dutchman Summerville scored 21 goals in all competitions last season as Leeds missed out on promotion with defeat to Southampton in the play-off final.
The Hammers have also held talks with Borussia Dortmund in a bid to sign Germany striker Niclas Fullkrug.
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