The Saints captain is set to leave the club this summer following their relegation from the Premier League last season.
His experience in the top flight is highly valued and several Premier League clubs are interested in snapping up the 28-year-old midfielder.
West Ham boss David Moyes is a big fan of Ward-Prowse and wants to add him to his post-Declan Rice midfield ahead of next season.
But it has been claimed that Fulham have now entered the fray to get their hands on the Southampton captain.
The Cottagers are lining up a replacement for Joao Palhinha, who has emerged as a major target for West Ham.
Ward-Prowse is being courted by Fulham and they have the advantage over the Hammers in the race.
The midfielder is claimed to be preferring a move to Craven Cottage over the London Stadium this summer.
Southampton want a deal worth £30m for their star man who has three years left on his contract.