El Mundo Deportivo says Mourinho asked president Florentino Perez about signing Eto'o over the summer, but the deal was a non-starter.
However, now with Inter struggling, Mourinho has discussed with Perez trying for Eto'o next month. The intention is to wait until mid-January for results on Gonzalo Higuain's back injury before making a move for the Cameroon superstar.
Even with Eto'o Cup-tied from the Champions League, Mourinho would welcome him to Madrid and has already made contact to alert his former Inter star to his thinking.
Despite his past with Barcelona and his taunts aimed at Real during his time at the Nou Camp, Eto'o would love the chance to be reunited with Mourinho.
Eto'o has already apologised for his rants against Barca: "I never meant any disrespect to Madrid, the club that brought me to Europe and I'll always be grateful. It was a mistake and I apologize."