The former Spain international striker is working on a deal to play for the North American Soccer League side, according to the club's manager.
Raul, 36, will see his two-year contract as a player and youth director with Qatari club Al-Sadd come to an end after this season. He had previously spent two seasons at German side Schalke following a 16-year career with Real Madrid in which he made 550 appearances for the Spanish giant.
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The former Spain international is looking to become a coach when his playing days come to an end, but a report out of South America suggests that he would like to keep playing in the American league.
Savarese told El Universal that both the Cosmos and Raul were working on a deal.
"There is mutual interest and it is pretty close to becoming a reality," Savarese told the paper. "If an agreement is reached it would be interesting -- important from a footballing point of view for what he can still give on the field, and in the dressing room, and also because he would enrich the group."
Former La Liga pair Marcos Senna and Ayoze Garcia currently play for the Cosmos.