James has struggled for game time and form this season, and his prospects have not improved under new manager Zinedine Zidane.
He has played just 54 minutes in the Frenchman's first two games in charge, and Zidane is reportedly unimpressed with the 24-year-old's attitude, per Sport's Alejandro Alcazar.
Los Blancos only signed James in July 2014, and his first season at the Bernabeu was excellent—he netted 13 La Liga goals and provided 13 assists, per WhoScored.com.
Will James Rodriguez join Manchester United in 2016?
However, he struggled for a regular starting place under previous manager Rafael Benitez and is not faring much better under Zidane.
James is a player of immense quality, and he would be a fantastic addition to the United squad if he could find his best form.
At his best, he is one of the premier players in the world, and he would arguably be worth the mooted price of more than £60 million if he could find his top level at Old Trafford.
The Red Devils have lacked attacking invention under manager Louis van Gaal, and James could be very helpful in solving that problem.
However, with the recent news that Los Blancos have been handed a two-window transfer ban, United will surely fail in their attempts to sign James.
As Bleacher Report's Sam Tighe and Dean Jones report, it's unlikely any Real stars—specifically Cristiano Ronaldo—will be departing the club, as it will not be possible to bring in high-class replacements:
The same will surely be true of James, who, while currently out of form, is undoubtedly one of Madrid's top players.
Elsewhere, United target Robert Lewandowski reportedly wants a move away from Bayern Munich, as he is unhappy about the impending arrival of Carlo Ancelotti as manager at the Allianz Arena in the summer, per Fichajes (via the Daily Star's Alex Wood).
The report indicates that Lewandowski is valued at £70 million, but he would prefer a move to Paris Saint-Germain over the Red Devils.
The Pole would be a brilliant addition at United.
The Manchester outfit have struggled hugely for goals this season, but Lewandowski has netted 15 in 16 games and could be a huge help to the United attack, per WhoScored.
However, it does not seem likely that Bayern will be open to letting him go—his current contract runs until 2019—and the striker himself would surely be loath to leave the Bundesliga giants given their trophy-winning prospects.