Sir Jim Ratcliffe is believed to be drawing up plans for the summer transfer window after acquiring a minority stake in the 20-time English champions.
Although there are likely to be a number of departures, the new Man United co-owner is also looking at areas of the pitch that need strengthening, including the centre of defence.
Raphael Varane and Jonny Evans are set to leave when their contracts expire in the summer, while Lisandro Martinez's injury issues are proving to be a concern.
According to inews, Man United are plotting to bolster their backline with two new central defenders ahead of the 2024-25 season.
The report claims the Red Devils are considering moves for Brazil international Bremer and Everton academy produce Branthwaite.
Bremer has made 71 competitive appearances since joining Juventus from their local rivals Torino in the summer of 2022.
The 26-year-old initially signed a five-year deal, before he penned a new contract in December to extend his agreement by a further 12 months to June 2028.
Despite appearing to commit his long-term future to Juventus, Bremer could still prove to be a relatively affordable option for Man United, with his deal said to include a €50m (£42.8m) release clause.
The Red Devils could face competition for Bremer's signature, with the Brazilian attracting interest from Real Madrid, Chelsea and Tottenham Hotspur.
The uncertainty surrounding Bremer's future has seemingly led to Juventus identifying Bologna's Riccardo Calafiori as a potential replacement.
In addition to Bremer, Man United are also admirers of Branthwaite, who has established himself as a key part of the Everton side this term.
Branthwaite, who spent last season on loan with PSV Eindhoven, has started 25 of Everton's 28 Premier League matches this season.
The 21-year-old is under contract until the summer of 2027, and Everton boss Sean Dyche has insisted the club are reluctant to sell the young defender.
As a result, the Toffees are determined to hold out for £75m, while Man United will look to negotiate a fee closer to the £50m mark.