The Hammers were strongly linked with either a loan or permanent move for the 30-year-old during the summer transfer window.
However, David Moyes's side were ultimately unable to reach a full agreement with all parties, while Maguire has dismissed suggestions that a transfer to the London Stadium was ever close.
Maguire has become a peripheral figure at Man United since the arrival of manager Erik ten Hag at the start of last season, and has fallen behind fellow centre-backs Raphael Varane, Lisandro Martinez and Victor Lindelof in the pecking order.
The England international started just eight Premier League games for the Red Devils last season and has since started only two of the club's first 11 matches in all competitions this term.
Maguire, who was stripped of the Man United captaincy over the summer, recently admitted that his current situation at Old Trafford needs to change and has suggested that he may consider an exit if he continues to play "once every month".
Should Maguire's game time not improve heading into the New Year, a January transfer could therefore be on the cards with West Ham one club said to still hold an interest in the defender.
According to Football Insider, the Hammers are set to be in pole position to sign Maguire in the winter window if he decides to leave Man United.
The report adds that any potential deal in January would most likely be an initial loan with an option to buy.
Moyes is said to be keen to strengthen his squad in January by recruiting a new central defender, despite adding summer signing Konstantinos Mavropanos to his squad that also includes Nayef Aguerd, Kurt Zouma, Thilo Kehrer and Angelo Ogbonna.
However, it is claimed that West Ham are unable to afford splashing the cash on a big-money signing in the New Year and would need Maguire to reduce his £200,000-a-week salary if he agreed to join the club.
West Ham could face competition for Maguire's signature from a number of Serie A clubs including AC Milan, who are understood to have expressed an interest in the defender.
Maguire, who played the full 90 minutes in England's 3-1 win over Italy in Euro 2024 qualifying on Tuesday, is under contract at Old Trafford until the summer of 2025.