The World Cup winner helped the club to lift the FA Cup trophy over the weekend, starting alongside Martinez in defense.
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Martinez posted on Instagram: "Brother, thank you for these two years we spent together, it was really a pleasure playing alongside you, I learned a lot. I wish you all the best, Rapha! You are a great one."
The Argentine will now be waiting to see who the club bring in this summer to replace Varane.
The Red Devils have been linked with a host of center halves, including Fulham's Tosin Adarabioyo.