Shelvey, 21, may be sold on by the Reds this summer after an underwhelming second half of last season when he struggled to force his way into Brendan Rodgers' side.
The former Charlton youngster, who scored the winner last term against the Hammers in a 3-2 win for the Reds at Upton Park, was below-par when he did get a chance under Rodgers and it is thought the Northern Irish boss is now prepared to let the youngster leave despite the fact he signed a new, long-term deal just 12 months ago.
He has fallen behind Jordan Henderson, Joe Allen and Lucas in the Liverpool central-midfield pecking order and could be sold if a club matches the asking price - thought to be at least £6million.
The Hammers are interested should Shelvey be made available for transfer but they would face competition from both Norwich and Swansea.
A move back to his London roots may be attractive to the England Under-21 star, however, and West Ham may well be favourites to land him should Liverpool decide to sell.
West Ham last week