They have identified England international James Ward-Prowse as a perfect fit but a deal doesn’t look easy for him.
Southampton want £40 million for the 28-year-old who has a contract until 2026. But the Hammers value him at £25m – £15m short of the Saints’ asking price.
West Ham hoped to smooth negotiations over Ward-Prowse by letting Flynn Downes move to St Mary’s.
The Hammers signed Downes last summer for £12m, but manager David Moyes is unsure whether he can fill the void left by Rice’s departure.
However, the Daily Mail report the Hampshire outfit are only interested in a straight cash deal for their captain.
He has been one of the best players to emerge from the Saints’ youth academy.
Ward-Prowse made his senior debut in 2011 and has since made over 400 appearances for the English club.
The experienced midfielder has been one of the key players for Southampton since they won promotion to the Premier League in 2012.
He consistently delivered excellent performances to help them stay in the English top-flight.
However, Southampton suffered relegation to the Championship last season after finishing bottom of the table.
Several of their top players are expected to leave the club, including Ward-Prowse. Fulham are also keen to sign the England international.