The 27-year-old has been in impressive form for the Old Lady during the 2023-24 campaign, making 37 appearances in all competitions, scoring three times in the process.
Bremer has a contract in Turin until June 2028, but there is believed to be a £51.5m buy-out fee in his deal, with Juventus in a vulnerable position heading towards the summer market.
According to the Daily Mail, Man United are considering activating the release clause in his agreement, with the Red Devils huge admirers of the Brazil international.
Bremer started his professional career at Atletico Mineiro in 2017 before making the move to Torino, and he spent four years with the club ahead of a switch to Juventus.
Man United 'interested in summer deal for Bremer'
The South American has represented his current side on 80 occasions in all competitions, scoring eight times, including a goal against Roma in Serie A on Sunday.
Man United are expected to move for two new centre-backs this summer, with Everton's Jarrad Branthwaite thought to be their leading target in that area of the field.
However, the Toffees could price the Englishman out of a move at the end of the season despite their financial problems, having secured their Premier League status for 2024-25.
Bremer is believed to be on a list which includes Nice's Jean-Clair Todibo and Benfica's Antonio Silva.
Meanwhile, Premier League duo Max Kilman and Marc Guehi, who represent Wolverhampton Wanderers and Crystal Palace respectively, are also allegedly being considered.
What is the centre-back situation at Old Trafford?
Raphael Varane and Jonny Evans are both out of contract at the end of June, and the pair are widely expected to depart when their deals expire.
There is also uncertainty surrounding the futures of Harry Maguire and Victor Lindelof, with both players believed to be available for the right price this summer.
Lisandro Martinez will stay, while Willy Kambwala is also set for a first-team role next season, but the Red Devils are certainly in need of a boost in the middle of their defence.
There will not be money in the budget for two big-money arrivals in that area of the field, so Man United will need to be inventive when it comes to the market.
As it stands, Varane, Maguire, Lindelof, Martinez and Kambwala are all on the treatment table, with Evans, who is only just back from a muscular issue, starting alongside Casemiro in the middle of the defence against Crystal Palace on Monday night.