The Irons are believed to have resumed talks over a deal for the former Red Devils captain, having seen a £30m transfer break down earlier this month.
With Maguire needing to accept a £70,000-a-week pay cut in order to move to the London Stadium - where he would pocket £120,000 in weekly wages - he is thought to be demanding a sizeable payoff from Man United.
The 30-year-old's contract at the Theatre of Dreams runs for another two seasons, and Man United's first offer of a £6m payoff was allegedly deemed insufficient by Maguire, who wants a larger sum to leave the club.
West Ham have supposedly shown a willingness to up their initial £30m offer in order to help fund Maguire's payoff, but according to talkSPORT, Man United will still turn down the Irons' most recent approach.
While Man United would have been happy to offload Maguire earlier in the window, the report claims that Raphael Varane's recent injury means that Erik ten Hag is desperate to retain his services.
Varane was withdrawn at half time in the weekend's win over Nottingham Forest, although it is still unclear how severe the Frenchman's issue is, and Victor Lindelof was chosen to replace him over Maguire against the Tricky Trees.
However, with left-back Luke Shaw - who has also usurped Maguire in the central pecking order - out for a number of weeks owing to an injury of his own, the Red Devils are facing a mini-injury crisis in the heart of the backline.
With Phil Jones and Axel Tuanzebe already departing as free agents, Ten Hag may only have Lisandro Martinez, Eric Bailly, Lindelof and Maguire as his centre-back options for Sunday's trip to Arsenal, and any West Ham bid for the latter will therefore be rebuffed.
Furthermore, Bailly is expected to leave for Saudi Arabia before the end of the window, while the Red Devils are yet to agree a one-year contract with Jonny Evans following his return to the club in pre-season.
Even before Shaw and Varane's injuries, Ten Hag affirmed on multiple occasions that he wanted to keep hold of Maguire, despite stripping him of the captaincy following the end of the 2022-23 season.
The former Leicester City man started just eight Premier League games and three Europa League contests for Man United last term, and he is yet to earn any competitive minutes this season either.
Despite hitting a roadblock in payoff negotiations with the club, Maguire is understood to have been open to an exit, as England boss Gareth Southgate has warned him that his spot in any Euro 2024 squad could be in jeopardy unless his playing situation improves.
Maguire boasts a total of seven goals and five assists in 175 matches for Man United since his £80m arrival in 2019, which remains the world-record fee for a defender.
After failing with their first bid for Maguire, West Ham instead signed former Arsenal centre-back Dinos Mavropanos, agreeing an £18m deal with Stuttgart for the Greece international.