The 50-year-old former Chelsea manager saw his side exit the Champions League after a 4-3 aggregate defeat by Borussia Dortmund in the semi-final.
The Portuguese has been linked with a move away from Spain and has spoken in the past of a return to England.
After the match in Madrid he said: “I know in England I am loved, I know I am loved by some clubs, especially one.”
Mourinho left the Blues in acrimonious circumstances after a falling out with owner Roman Abramovich, although Mourinho remains Chelsea’s most successful manager with two Premier League titles and three domestic cup wins.
Current interim Chelsea boss Rafael Benitez, an unpopular figure among Blues supporters, has said he will leave the club at the end of the season.
Mourinho added: “I am loved by the fans and the media who treat me in a fair way.
“I know in Spain it is different because many people hate me.”
Real are 11 points behind arch rivals Barcelona with five games remaining in La Liga.
They face city rivals Atletico in the Spanish Cup final in May, Real’s last realistic chance of winning silverware this season.
Mourinho insisted he would wait until the end of the current campaign before making a decision on his future.
“I didn’t make a decision because I have a contract and the respect I have for the club and the president,” he said.
“At the end of the season I want to sit down with the president and speak about it.”