Harry Maguire, 30, struggled for first-team opportunities at Old Trafford last season and has been stripped of the captaincy this season.
Harry Maguire is understood to be keen on the move with personal terms yet to be agreed but not expected to be a problem.
Harry Maguire joined United in August 2019 for a world record £80m for a defender.
West Ham have been trying to sign Ward-Prowse for much of the summer but Southampton, who were relegated to the Championship last season, had rejected their advances until this point.
However, it has appeared inevitable that Southampton would lose their captain and that now seems set to happen.
Harry Maguire trained with Man Utd on Wednesday morning ahead of their Premier League opener against Wolves on Monday Night Football.
United have done due diligence on several defenders, including Jean-Clair Todibo of Nice, should they be in a position to sign reinforcements at centre-back for Maguire and Eric Bailly, whose representatives have held talks with Al Nassr.
Moyes also wants a centre-back and has convinced the board to move for Maguire. West Ham have an agreement in principle on a fee of £30m for Maguire and are due to discuss personal terms with the defender. The 30-year-old has fallen out of favour under Erik ten Hag, who has stripped of him of the captaincy, and needs to move to try to protect his England place.
One potential stumbling block for West Ham is that Maguire, whose deal runs until 2025, received a considerable salary increase as a result of United qualifying for the Champions League. West Ham have been looking for a way to ensure they and United can cover any potential shortfall in Maguire’s wages.
Despite his struggles at Manchester United, Harry Maguire has been a regular for England under Gareth Southgate, starting all five games at the 2022 World Cup.
Ward-Prowse started Southampton's Championship opener against Sheffield Wednesday on Friday but did not play in their Carabao Cup first-round defeat against Gillingham on Tuesday.
Rice's departure leaves West Ham without an obvious captain and Moyes has opted not to name a replacement so far, but Maguire and Ward-Prowse provide two options.
Current first choice central defenders Nayef Aguerd and Kurt Zouma have both had injury problems in recent months.
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