Rodriguez has endured a difficult season at Real Madrid.
The Colombia international has struggled to establish himself in Zinedine Zidane's starting XI.
Rodriguez has made just nine La Liga appearances so far, scoring once.
The most surprising transfers in football
Thu, October 20, 2016
Express Sport takes a look at some of the most surprising transfers in the Premier League, the Football League and around the world in recent history
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Express Sport brings you a collection of the strangest transfers in recent history
James Rodriguez could be off to Chelsea in the summer
Real Madrid have long been admirers of Eden Hazard
And Spanish outlet Diario Gol claim Madrid are willing to offer him to Chelsea to land either Thibaut Courtois or Eden Hazard.
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Madrid want to sign Courtois with Keylor Navas expected to leave at the end of the season.
And the Champions League holders also retain an interest in Hazard, who has scored 11 goals for the Blues so far this campaign.
Rodriguez could be used to broker a deal for either of the Chelsea duo.
James Rodriguez has scored just one league goal for Real Madrid this season
However, Madrid also have two other transfer deals that the former Porto and Monaco star could be used in.
The Spanish giants want to sign Juventus star Paulo Dybala – and are considering using Rodriguez as bait to land the Argentina international.
Madrid are also interested in Bayern Munich's David Alaba and could offer the playmaker to the Bundesliga side to tempt them into selling.