Lopetegui is under increasing pressure at Madrid, after seeing a win-less run stretched to five games with defeat at home to Levante on Saturday.
Spanish outlet, El Chiringuito reports that Real Madrid’s Directors have identified Mourinho as their number-one target to replace Lopetegui before the end of the season following the Los Blanco’s poor run of results this campaign.
Mourinho spent three years with the Champions League holders during his time at the Spanish capital.
Portuguese gaffer won the La Liga and the Copa del Rey before returning to England for a second spell with Chelsea.
The 55-year-old has also been struggling with his current club, Manchester United in the English Premier League this term.
Mourinho’s side currently sits at the 10th position on the Premier League log after nine games.