Harry Maguire played in 31 of Manchester United's 62 games in all competitions last season.
The 30-year-old England defender has an uncertain future at Old Trafford as Raphael Varane and Lisandro Martinez have emerged as Erik ten Hag's first-choice centre-backs.
Maguire revealed on Sunday that he had been stripped of the captaincy at Old Trafford, saying he is "extremely disappointed" to have lost the armband after three and a half years.
Maguire's contract runs to 2025.
United also need to sell players to boost Ten Hag's chances of reshaping his squad in the current transfer window as he closes in on Inter Milan goalkeeper Andre Onana.
The centre-back arrived at United from Leicester City for £80m in 2019, but is known to be among the players Ten Hag would now sell if a suitable offer came in.
Maguire is mindful of needing to play regularly next season before Euro 2024 in Germany next summer. However, he is known to be happy at Old Trafford and is proud of his status as captain.
In addition, after overcoming a number of injury issues last term, Maguire feels he will play a full part in United's season.
West Ham manager David Moyes is keen to make additions to his squad following the sale of skipper Declan Rice, which could generate £105m.
Moyes is interested in Ajax's Mexican midfielder Edson Alvarez as a possible replacement for Rice, but Maguire would be a useful addition at the back, where both members of West Ham's first-choice pairing - Kurt Zouma and Nayed Aguerd - suffered injury issues last season.
-- Courtesy of BBC Sport