The Hammers are in the market for a player to lead their line next season after failing in their efforts to bring in Celta Vigo's Maxi Gomez, who turned them down to join Valencia instead.
Sky Sports claims that the Premier League side have opened discussions with the Bundesliga club over Haller’s potential transfer.
The Frenchman is valued at £40 million after scoring 20 goals in all competitions during the 2018/19 campaign.
Haller directly contributed to 24 goals in the Bundesliga last season (15 goals, nine assists), and only three players managed more.
Haller’s representatives are on standby as the two clubs look to thrash out a deal, and will fly to London to discuss terms once a fee is agreed.
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