BBC Sport has been told Bayern have accepted a bid from United of £38.6m plus £4.3m in add-ons for De Ligt, who was captain of Erik ten Hag’s Ajax side that reached the Champions League semi-final in 2019.
In addition, they are set to pay £12.9m for 26-year-old Morocco defender Mazraoui.
United have targeted central defence and right-back as key areas to strengthen in Erik ten Hag’s squad.
Ten Hag said last weekend the club’s new hierarchy were “eager” to do deals.
Mazraoui’s arrival had been linked to the exit of right-back Aaron Wan-Bissaka, who moved to Old Trafford from Crystal Palace for £50m in 2019.
The Red Devils have now agreed a deal with West Ham for Wan-Bissaka and the 26-year-old will have a medical with the Hammers on Sunday.
United had two bids for Everton’s England international Jarrad Branthwaite turned down earlier in the summer.
With the Merseyside club sticking to their £70m valuation, De Ligt, 24, is considered a cheaper option and has more experience.
Both De Ligt and Mazraoui played in front of United goalkeeper Andre Onana during their time at Ajax.
De Ligt joined Juventus in 2019 for £67.5m and after winning one Serie A title and one Coppa Italia in 117 appearances he joined Bayern in 2022 for £65.6m.
He has played 73 games for the German side and won the Bundesliga.