Chelsea supporters sang for the coach known as the 'Special One' during Saturday's 1-1 FA Cup draw with second-tier Birmingham City after the Inter faithful had done the same in Friday's 3-0 Serie A defeat at home to Bologna.
The results piled more pressure on Chelsea's Andre Villas-Boas and Inter's Claudio Ranieri who was also succeeded by Mourinho at Stamford Bridge back in 2004.
"My message to the fans is I love Chelsea and Inter a great deal but I would prefer them to support their own teams and coaches," Mourinho told a news conference after Real's 4-0 La Liga win at home to Racing Santander.
"I am the past, a very good past, but I am not there anymore and they should all be fighting together."
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