Rodriguez is currently on a two-year loan at Bayern Munich.
But that’s not stopped bookies Ladbrokes tipping him for a summer switch to Old Trafford.
Jose Mourinho’s side are 6/4 favourites to get the Colombian superstar, who could put himself in the shop window at the World Cup in Russia.
Chelsea are second-favourites at 5/2 with PSG 3/1 to get the attacking ace.
A switch to any Chinese club comes in at 5/1 with a move to Italian giants AC Milan 6/1.
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“Man Utd are 6/4 favourites to get James Rodriguez”
Alex Apati of Ladbrokes said: "James has hardly touched down in Munich but it looks as though his time in the Bundesliga will soon be over with a whole host of European heavyweights thought to be eyeing up a move."
Rodriguez might have been tipped for a move, but the player says he’s happy at Bayern.
Speaking last month, the 26-year-old said: “It's a new way of life for me, but I’m happy.
"It's more chilled out here - I can go out for a walk without being pestered - and I'm learning German.
“And, of course, Bayern are a massive club who are always challenging for honours."
Rodriguez added: "I hope to win titles and show people what I'm capable of on the pitch.
"I'll give everything - right until the last. I want to win titles with this fantastic club!"