The cash conscious Hammers are keeping a tight grip on their wage bill but are ready to discuss terms with the player.
The board have regularly made it clear the need to hold down their wage bill and that could scupper a deal for the player who has now had spells at Bolton and on loan at Sunderland last season.
The Hammers have no problem with a £1.5 million fee and Alonso is ready to quit Fiorentina for London.
He enjoyed an impressive spell on loan at Sunderland last season and is believed to be looking for a deal in the region of £40k a week.
A Hammers source told ClaretandHugh: “There’s no problem with the transfer fee but it’s in the wages area that the problems arise so it’s all very much in the balance.”