The 27-year-old was heavily linked with a move to Old Trafford earlier this summer following the arrival of Dan Ashworth as the Red Devils' new sporting director.
The highly-rated centre-back signed for I Bianconeri from Torino two years ago for a fee of around £38m.
He was included in the Serie A Team of the Year for two consecutive seasons after being named the league's best defender at Torino in 2022.
Reports indicated that United were willing to include Mason Greenwood as part of a potential deal for Bremer, but it seems the Brazilian international now has no interest in a summer move.
Juventus confirm Bremer contract extension
Earlier today, Juventus revealed that Bremer has renewed his contract at the Allianz Stadium, extending his stay in Turin until June 30, 2029.
Posting on their official club website, Juve wrote: "None of this would be possible without his undeniable talent, which he shows every time he sets foot on the pitch, but his work ethic and commitment are just as important, always putting himself at the disposal of the team and coaching staff every day.
And so, we are delighted to say that we are continuing together with Gleison Bremer!"
Shortly after the announcement, transfer expert Fabrizio Romano added that the club has also amended the 27-year-old's release clause as part of his deal, with the new figure now moved up to around £51m.
Bremer had previously hinted at remaining in Serie A for the 2024-25 campaign, telling Romano last month, "I'm already at a top club, I'm already at Juventus. We'll achieve great things next season. Thiago Motta is an excellent manager and a very good choice."
Man United to step up pursuit of Bayern Munich duo?
With Bremer now set to remain in Turin for the foreseeable future, Man United are likely to look elsewhere for defensive reinforcements, with the club heavily linked with moves for Bayern Munich duo Matthijs de Ligt and Noussair Mazraoui.
The Red Devils signed 18-year-old Leny Yoro last month but the talented teenager is now set to miss up to three months after sustaining a foot injury during pre-season.
Widespread reports in recent days suggested that Erik ten Hag's side had tabled a joint offer in the region of £51m for the Bayern defensive pair, but the Bavarians are believed to have rejected the bid as it did not meet their valuation.
It is understood that the German giants are willing to allow both players to leave this summer but are looking for a fee closer to £64m to consider parting ways with them.
Bayern are said to have informed both De Ligt and Mazraoui that they are not part of Vincent Kompany's plans for the upcoming season.