During the 2020-21 season, the 23-year-old scored 12 goals in 32 appearances for the Blues, but he struggled to find regular playing time under Thomas Tuchel.
Aston Villa are reportedly interested in signing the Englishman on a permanent basis, with Dean Smith’s side reportedly in advanced talks over a £38 million deal.
The Hammers, however, have moved to the front of the queue, according to Football Insider, as David Moyes’ side looks to bring a new striker to the London Stadium.
Abraham could be available for £35 million, according to the report, which West Ham would be willing to pay despite Moyes previously stating that his club would struggle to afford him.
The Englishman, who has two years left on his Chelsea contract, has scored 30 goals in 82 appearances in all competitions for his current club.