The Independent is reporting that the Red Devils have “stepped up” talks to try and sign the 25-year-old Colombian this summer.
The same report claims that Rodriguez would likely cost less than Alvaro Morata, who has been heavily linked with a big-money move to Old Trafford throughout the summer.
The story also suggests that Real Madrid are likely to want a fee in the region of €70m for Rodriguez this summer if they are to let the midfielder leave The Bernabeu.
Manchester United have been linked with a host of players this summer including Morata, but the Red Devils confirmed on Saturday morning that they had agreed a fee with Everton to sign striker Romelu Lukaku.
The Red Devils jetted off to the United States for their pre-season tour on Sunday as Jose Mourinho prepares for his second season in charge at the Old Trafford club.
Manchester United will make a return to the Champions League next season after they won the Europa League last term.
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