Zakaria is said to be a target for a host of European clubs but Man United are the frontrunners, according to Sky Germany (via the Daily Star).
The Swiss international is reportedly attracting interest from Atletico Madrid, Borussia Dortmund and even United's biggest rivals Liverpool.
Borussia Monchengladbach are keen to keep hold of the 23-year-old as he is seen as a key cog in the heart of the side's midfield.
"I think that there is a very good chance that Denis will still be with us next year if we qualify for the Champions League," sporting director Max Eberl recently said.
Zakaria has made 88 appearances for Gladbach since he joined from Swiss outfit BSC Young Boys in 2017.
He also has 28 caps for Switzerland and will likely be a part of their Euro 2020 squad this summer.
The Red Devils have improved their form of late, no small part down to January signing Bruno Fernandes, whose influence has been pivotal.
Ex-Manchester City defender Micah Richards believed that Fernandes could do with some new faces around him.
"At some stage you’re going to need a little bit more quality," Richards said on Sky Sports.
"We mentioned bridging the gap - these players have done well and they’re probably an easy group to manage.
"But if they want to be competing, they’re going to have to buy a little bit more quality."
United boss Ole Gunnar Solskjaer is pleased with how his team appear to be turning over a new leaf.
"We feel we are improving all the time," Solskjaer told the media
"We know we lack one, two, three players to be considered a title contender and some experience.
"We are just going to start talking about going up the table, getting more points."
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Quiz! Can you name every club to reach a Champions League or European Cup final?
