Veteran striker Costa is available as a free agent following his exit from Brazilian side Atletico Mineiro at the start of 2022.
The former La Roja international has been linked with a return to Spanish football alongside potential moves to Turkey, Saudi Arabia and England.
However, the controversial hitman has not reached an agreement with anyone and remains available ahead of the 2022/23 season.
Rayo have been locked in talks with the 33-year-old and his representatives, over a one-year deal back in Vallecas, with a €1m annual salary.
The former Chelsea star won over the Rayo fans, after netting 10 goals in 16 games on a six month loan move from January 2012, to save them from top-flight relegation.