The 32-year-old defender is entering his seventh season at Old Trafford since his record 80 million pounds move from Leicester City in 2019. United exercised an option in January to extend his contract until 2026, preventing him from leaving as a free agent.
Despite that, interest from clubs persisted. Maguire confirmed that multiple teams - including Premier League and Serie A sides - made contact, but United gave a "quick response" to shut down any talks.
"I think there were a couple of clubs who enquired, or spoke with (United), and I think they got a quick response," Maguire said.
"The club made it clear I can't leave under any terms."
Speaking at a Manchester United Foundation event, Maguire gave further insight into his mindset and potential future at the club. While he didn't start in United's season opener against Arsenal - coming on as a late substitute behind new signing Matthijs de Ligt, Luke Shaw, and Leny Yoro - he remains confident he'll play a big role this season.
"I'm sure there's going to be many games I play this season. I know I'm going to start a lot of them," he said.
"The squad is really competitive now. There's tough choices for the manager, and healthy competition in every position."
While no extension beyond 2026 has yet been agreed, Maguire hinted that he's open to staying at United long-term.
"I'm sure over the next few months they'll sit down and we'll have to have a conversation - whether they want to extend (my contract) or if something changes in January," he said.
"I have something in my mind about what I want to do, but I don't want to put it out there to everybody.
It's an amazing club to play for, and you'd be silly to want to jump out of it as soon as you could."
Maguire acknowledged that last season's contract extension was fully in the club's control, but this time around, discussions will need to be mutual.
"Last year, the clause was in their hands. They activated it, and that was that. This year, obviously I'm up at the end of the year, so things are a bit different."
How much playing time he gets in the first half of the season - especially with no European football to increase rotation - could be pivotal in determining whether he signs a new deal or reconsiders his future in January, when he would be eligible to talk to foreign clubs if no agreement is reached.