The 32-year-old goalkeeper joined Malaga from Elche in 2011, and has made 117 league appearances in that time.
Caballero has been heavily linked with a move to Manchester City in recent weeks, with some reports suggesting the keeper is set for a medical at the Premier League champions in the coming days.
And on Sunday, Caballero appeared to be bidding farewell to the Malaga fans, although he held back from confirming news of any move.
"I am reading everything you [the supporters] write," he posted on his official Twitter account.
"I express my gratitude for that from the heart.
"But I am not going to say goodbye from here, I would like to do it the right way."
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