Goal.com UK exclusively revealed Yakubu was set to become one of Grant's first signings once he was confirmed as Hammers boss.
Reports in The Mirror now suggest that The Hammers have tabled a £4m bid while the Merseyside club are refusing to contemplate selling their man for any less than £6m.
David Moyes will be aware that his transfer budget for the summer depends on how much money he is able to get into the club, and this will make him determined to dig his heels in for extra cash.
Yakubu cost £11.25m from Middlesbrough in 2007 but his time at Goodison Park has been disrupted by injuries and he has only netted nine times in 35 appearances.
West Ham are expected to increase their bid this week in an effort to land their man.
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