The Wales midfielder has ended his deal with Pumas by mutual consent, says ESPN.
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Ramsey made just six appearances for Pumas and has been struggling with a hamstring injury during the season.
Pumas are 13th in the league table, and there are two matches left in the regular season. They need to finish in the top 10 to secure a spot in the league's play-offs.
Ramsey has also lost his pet dog, Halo, while in Mexico, offering a £15,000 award for it's return. Halo has been missing since October 9.