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The Colombian joined Real for a reported 80 million euros from Monaco ($84 million) after starring as the top scorer at the 2014 World Cup.
However, after a fine debut campaign, Rodriguez has been marginalised in the past two seasons and was an unused substitute as Real won the Club World Cup with a 4-2 win over Japanese champions Kashima Antlers in Yokohama on Sunday.
"I have to be calm and I have seven days to be able to reflect on it," Rodriguez told reporters after the final.
"I want to be here but sometimes things don't work out. I have to think about it all and I can't guarantee if I will stay or not because I want to play more."
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Rodriguez has started just four times in La Liga this season as Real have shot to the top of the table on a club record 37-game unbeaten run in all competitions.
Since Zinedine Zidane took charge in January, the 25-year-old has fallen behind more unheralded names such as Lucas Vazquez, Isco, Casemiro and Marco Asensio for a place in Real's midfield.
However, any exit may be complicated by the fact Real won't be able to immediately replace him unless the Spanish giants' appeal against a one-year transfer ban for irregularities in the signing of players under 18 is upheld by the Court of Arbitration for Sport.