The Spanish club are thought to be desperate to bring the Spain forward back to the La Liga outfit before the January transfer window closes on Monday evening.
Now, The Sun is reporting that Atletico are prepared to let Martinez leave the club to join Chelsea in a deal which would see Costa head the other way.
The same newspaper report also claims that Costa regularly speaks to his former team-mates and would be keen on a return to the Spanish club.
However, the story goes on to say that Chelsea are unlikely to want to complete the deal, as neither player would be eligible to play in the Champions League this season if it went through.
Costa, 27, has scored eight goals and made three assists in 19 Premier League games for Chelsea so far this season.
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