The midfielder's contract runs out in 2025 and he reportedly wants a raise but Real are not willing to increase his salary.
The Blues are keeping an eye on the situation and could make a move if the Brazil international chooses to move on.
The 30-year-old and his representatives are willing to sit down with Real chiefs after the final to discuss his future.
Los Blancos take on Quadruple chasers Liverpool in the final at the Stade de France in Paris on May 28.
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