The Hammers are refusing to boost their provide previous an preliminary payment of £37m plus £3m in add-ons for the Chelsea academy graduate, who's believed to be surplus to necessities.
The 23-year-old also has interest from Tottenham and can be open to leaving Stamford Bridge having been provided out to golf equipment for the final six months.
Everton proposed a £45m swap in January, which was accepted by Chelsea however Gallagher was unwilling to maneuver to Goodison Park.
The England midfielder has simply two years left on his contract and hasn't been provided a brand new deal.
Chelsea wish to exchange Gallagher with Brighton midfielder Moises Caicedo however have struggled to make progress in talks.
Brighton consider Caicedo's worth is just like that of Declan Rice, who West Ham bought to Arsenal for £105m and at the moment are making an attempt to exchange with two midfielders, together with Gallagher.
The Blues are open to signing multiple midfielder subsequent month with Ajax's Mohammed Kudus just lately sounded out.
Celta Vigo's Gabri Veiga, Everton's Amadou Onana and Southampton's Romeo Lavia are additionally on the shortlist.
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