The Hammers are badly in need of a striker following the departure of Sebastien Haller who joined Ajax this month for around £20 million.
Michail Antonio remains the only recognised striker at the club and David Moyes is keen to bolster that area.
West Ham have been linked with a host of strikers this month, including Josh King, Gaetan Laborde, Youssef En-Nesyri et al, and it seems they have earmarked Edouard as a potential option as well.
Edouard, who joined Celtic from Paris Saint-Germain in 2018, has scored 74 goals in 151 games for the Bhoys, but the Frenchman has not been at his best this season.
The 23-year-old striker has reached the final 18 months of his contract, and he is looking to test himself in the Premier League.
Although he wants to join a top-six Premier League club, the striker ‘fancies a move to London’.
Tottenham Hotspur and Arsenal are also reportedly keen to sign the striker who would cost in the region of £35m.
Tottenham boss Jose Mourinho gave an indication that he is not interested in signing a striker this month, when asked about whether Spurs are planning to move for Danny Ings.
Carlos Vinicius has done well as a back-up striker, and Spurs do not feel the need at the moment to sign a new player in that position. The situation could change in the summer if they do not sign Vinicius permanently and look for other options.
The situation is different with West Ham. Celtic could be interested in selling him if they get the right price but chances are very slim that the Hammers would pay such a high transfer fee this month for Edouard.