Mourinho's visit to London and Chelsea over the weekend has strengthened expectations of a return to Stamford Bridge in the summer.
Punto Pelota says four names are on Real president Florentino Perez's shortlist.
His first-choice is Borussia Dortmund coach Jurgen Klopp, who has already rejected overtures from Chelsea in recent months. PSG's Carlo Ancelotti, who is likely to leave France in the summer, also is among the names, having been a long-term target for Florentino.
Is Florentino's shortlist missing anyone? Give us your shout below...