The Colombia striker, however, insists he's not planning to retire.
After defeat to Barcelona, Falcao said: "My contract expires on June 30th and then I will see what options I will have. I feel good, I want to continue playing, so we will analyse the situation carefully, me and my family, which weighs a lot in this decision.
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"There is nothing that has been discussed with the club. Remaining in La Liga is an extremely important thing for this club, especially for its fans who always accompany us. Thank you for these three years and I wish Rayo many successes for the future."
Meanwhile, Diario Record says a move to Liga MX could be on for Falcao. A source said: "We can assure you that people very close to the Colombian say that the player would be enthusiastic about the idea of playing in Liga MX."