Mourinho is widely considered to be the front-runner to replace Louis van Gaal at Old Trafford in the event of the Dutchman’s sacking, with numerous reports suggesting that he has already signed a pre-contract agreement with the club.
Mourinho is said to be in the process of drawing up his transfer wish list ahead of his Man United move and Rodriguez tops it.
The Colombian joined Madrid in 2014 in a deal said to be worth £63m and he initially impressed during his debut campaign at the Bernabeu.
However, James has found chances harder to come by under Zinedine Zidane this term and he is reportedly growing frustrated at the lack of opportunities.
United may be put off following the failed transfer of Angel Di Maria last season but the fact is that James is a world-class talent and it is not often that one becomes available. United have money to spend and it would be spent wisely if they did sign the forward.