Manchester United paid a record £80m to make Harry Maguire the world's most expensive defender in 2019
The England defender, 30, looked set to join the Hammers after a £30m fee was agreed between the clubs.
Maguire struggled for first-team opportunities last season and was stripped of the captaincy this season.
However, United have maintained they would respect his wishes and did not want to push him out of the club.
A source close to the player said that while Maguire "respects West Ham and David Moyes" there was "never an agreement in place" over his personal terms.
They added: "Harry remains settled at United, loves the club and believes he will get plenty of opportunities to play this season."
Maguire was on the bench for United's 1-0 win over Wolves on Monday but did not get on even though manager Erik ten Hag used five substitutes and replaced central defender Lisandro Martinez with Victor Lindelof at half-time.
Prior to that game, Ten Hag said Maguire would be better off leaving United if he is not confident enough to battle for a first-team spot.
United paid Leicester City a record £80m to make Maguire the world's most expensive defender in 2019, with Pep Guardiola also keen to take him to Manchester City.
However, while he was given the captain's armband under former boss Ole Gunnar Solskjaer, he has endured a difficult time after a promising first campaign with the club.
An incident in Mykonos, in which he was given a 21-month suspended sentence for hitting a police officer and attempted bribery, appeared to impact his football.
A major fallout with Cristiano Ronaldo over the captaincy followed, while his Cheshire home was also the subject of a bomb threat.
And with his confidence appearing to be affected amid mounting criticism, he has even been subjected to jeers from some fans at certain games during pre-season, despite Ten Hag also saying he thinks Maguire is capable of playing a significant role this term.
"I feel like he is a quality player and I know that once he gets his confidence back, people stop ripping into him, and he's given a chance to showcase himself again, he will do well," Hammers forward Michail Antonio told BBC Radio 5 Live's Footballer's Football Podcast.
"How well and how quality the boy was playing to the stage where he is now - [he is] a shadow of the man, a shadow of himself.
"Leaving United could probably make him better because a lot of the stuff was coming from inside more than outside.
"I don't feel a change of manager could change his situation. He needs a change of club because he's got that stigma now to his name at United.
"Managers have changed and they've still not really wanted to play him. That stigma of Maguire at United is kind of stuck with him, so I think him stepping away, doing something else and having a new, fresh start can revive him."
-- Courtesy of BBC Sport