Serie A outfit Inter are reportedly in talks with Tottenham to bring soon-to-be free agent Eriksen to San Siro in January.
Eriksen – who is out of contract at the end of the season – is keen for a new challenge, having joined Spurs from Ajax in 2013.
Asked about Eriksen after he was booed by Tottenham fans during Tuesday's 2-1 FA Cup third-round replay win over Middlesbrough, Mourinho said: "He played very well. Played very well, very professional which is what I expect from him.
"If his decision is to leave, I think he has to leave with his head up, if he gives everything which is what he tries to do for the team.
"Fans, it's always to respect, we have to respect but I think the boy did it for us today."
While Eriksen's future appears away from Tottenham, Benfica midfielder Gedson Fernandes is reportedly close to arriving on loan from the Portuguese giant.
Amid talk of an initial 18-month loan deal, Mourinho said: "No news. I didn't want to know anything during the day.
"During the day it was just about the game. He doesn't have news for me so nothing."