The 25-year-old has enjoyed a stunning season for the Hammers, with an impressive return of 18 goals and 13 assists in all competitions on the wing.
United are facing a significant summer rebuild under incoming new manager Erik ten Hag and, with attacking players likely to be included on his wish list, Townsend believes Bowen could be a contender.
Speaking to Andy Goldstein on Drivetime, Townsend said: "Jarrod Bowen has been great. He's been so good lately.
"I tell you what, I bet you West Ham get a bid or two for him in the summer, I bet they do.
"Would you have him [at Manchester United]? Like a shot you should be saying.
"He can play anywhere. I've seen him play up the middle for West Ham, on one side. For your lot, he'd get in your team wherever he likes!
"I would play him off the right-hand side."
Signing Bowen would put big question marks over the future of Jadon Sancho, who has struggle to live up to the hype since his £73million arrival from Borussia Dortmund last summer.
And Townsend has urged the England winger to take a leaf from Bowen's book to improve his form for the Red Devils.
"Sancho's got to liven up, that's what he's got to do," he added.
"He's got to do more; he's got to do a lot more because he's had what, half a dozen decent game?"
With Bowen in fine form at club level, questions have also been asked regarding his chances of a call-up to Gareth Southgate's England squad for the World Cup in Qatar later this year.
However according to Townsend, that opportunity could be tough to materialise.
He said: "He's a good player, Jarrod Bowen.
"Should he be on the plane? He probably won't get on the plane, will he? It's just happened a bit late and I think that most of the seats on that plane are taken.
"With all of the players at the top of the field that Gareth has got to choose from, I don't quite see him getting on the plane unless he features in some of these Nations League games and plays unbelievably well.
"But he's a dangerous boy, there's no doubt about that."