According to the Daily Mail, Roman Abramovich has offered Grant his own former position - director of football - for significantly more than he stands to earn as West Ham boss.
Grant held the position before taking over as manager for Jose Mourinho in 2007.
Despite being sacked by Abramovich after losing the Champions League final to Manchester United, Grant remains close with the Chelsea owner.
Abramovich is prepared to exceed the £1.3million offered by West Ham to bring Grant back to Stamford Bridge.
It is believed Grant will be unveiled as West Ham boss next week despite interest in his services from Celtic and Dutch side FC Twente.
Grant also hopes to bring in a slew of Portsmouth players including veteran goalkeeper and possible managerial replacement David James.
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