Wrexham, owned by actors Ryan Reynolds and Rob McElhenney, will face Erik ten Hag's team in San Diego in July.
The game will form part of United's preseason tour of the U.S., which is likely to include Las Vegas.
Wrexham, meanwhile, are also in talks about a summer friendly with United's Premier League rivals Chelsea.
A statement issued by Wrexham, who are second in the National League, read: "The club can confirm that our previously publicised plans to tour the US during pre-season are at an advanced stage, but are not as yet finalised.
"Full details of the games the club will play in and where, will be released across the Club's communication channels when they are confirmed.
"We would advise fans against making any arrangements to travel to the games based on speculation, to avoid disappointment."
United have not toured the United States since 2018 when Jose Mourinho was manager. They last faced Wrexham in a competitive game in the FA Cup in 1995, a fixture that ended in a 5-2 victory for United at Old Trafford.