The Colombian has been strongly linked with a move away from the Bernabeu in recent months and Express Sport understands Manchester United and Chelsea are monitoring him.
Rodriguez was the subject of interest from the Premier League giants last summer after falling out of favour under Zinedine Zidane but a transfer never materialised.
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It's clear that in life and __football you never know what is going to happen but I want to remain here
James Rodriguez
The talented midfielder has been in and out of Zidane’s plans this term, but he has now poured cold water on Chelsea and United’s attempts to sign him at the end of the season.
“When I am given opportunities I always try and do well,“ he told Spanish publication AS.
“This is all I think about. I want to always be here.
“It's clear that in life and __football you never know what is going to happen but I want to remain here."
Rodriguez, who has scored five goals in all competitions for Real this season, is under contact with the Spanish outfit until 2020.