The New Zealand star, 28, signed a six-year agreement in 2015, but is now set to be handed a fresh deal.
Fonte, 33, moved from Southampton on wages of over £70,000 a week and Reid is among a number of the current Hammers squad set to be given similar.
Fonte’s January arrival has done little to improve West Ham’s defence and they have conceded in every league game since he joined for £8million.
Michael Antonio is one player revising his demands following Fonte’s arrival.
Antonio is the Hammers’ top scorer this season with nine goals in all competitions and is likely to ask for more money to reflect his contribution on the field.