The Red Devils are in the market for a central midfielder amid the club's ongoing struggles this season.
talkSPORT understands United are planning a marquee signing in the middle of the park this summer, amid links to West Ham and England star Declan Rice.
In the meantime, however, the club could look towards a budget option for the remainder of the season.
According to German broadcaster SPORT1, United have held talks over a January move for Zakaria, while Liverpool and Juventus are also interested.
It is claimed the Bundesliga side are willing to sell the Swiss international for between £5million and £6m.
United interim boss Ralf Rangnick knows Zakaria from his time in Germany.
The 25-year-old midfielder has made 118 appearances in the German top-flight, scoring 11 goals since joining from Young Boys in 2017.
He has represented Switzerland 38 times already, including at last summer's European Championship.
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