The Hammers are in desperate need for a striker this summer following Marko Arnautovic’s £20m switch to Chinese club Shanghai SIPG.
Andy Carroll has also been released while Javier Hernandez has been linked with an exit.
West Ham came close to securing a deal for Maxi Gomez earlier this month.
But after failing to agree to pay the full release clause, the 22-year-old instead joined Valencia.
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The east London side have since turned their attention to Haller, who scored 20 times for Eintracht Frankfurt last season.
The German club have confirmed that the Frenchman has travelled to London to complete a medical.
The two clubs have agreed a £45m deal and Haller will become their most expensive signing, eclipsing the £36m shelled out for Felipe Anderson last summer.
But Guardian journalist Jacob Steinberg has planted a seed of doubt by suggesting the deal could still be hijacked.
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“I don’t like being a heartbreaker but the deal isn’t 100% done yet,” he tweeted.
“Haller is on his way to London, terms all agreed with player and Frankfurt.
“But there is concern at West Ham at late interest in the striker from elsewhere.
“Am told his agent is in talks with another club.
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“Would still be confident of Haller sticking with West Ham.
“He is scheduled for a medical after all.
“But there’s no doubt West Ham are worried.”
After being questioned about the mystery club, Steinberg went on to confirm that it is not Manchester United.
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