The Italian champions beat Bayern Munich to win the Champions League on Saturday, making Mourinho the third coach to win the prize with two clubs.
But following the 2-0 victory at Real's Bernabeu stadium, Mourinho said: "I'm so sad as almost for sure it's my last game with Inter.
"If you don't coach Real Madrid then you always have a gap in your career."
The 47-year-old former Chelsea boss added: "It was difficult to leave Chelsea and it will be sad to leave Inter. Inter is my house in the same way Chelsea was my house. But that's life, that's football.
"Now I have two houses, Stamford Bridge, San Siro and now a third house - probably the Santiago Bernabeu.
"Only Real are interested in me but I haven't spoken with anyone and I haven't signed anything. I promised I'd speak after the final.
"I believe my target now is to win another championship that I've never won and win Champions League with a third club and then come back to England.
"Everybody knows that English football is my passion and I will go back to England once."
Mourinho, who joined Inter in 2008, has also won two Serie A titles and an Italian Cup.
"When I win I don't stop and here [in Italy] I have won everything. I've won the Champions League with two clubs and I can do it with three," he reflected.
"There are many things [in Italy] that I haven't liked and for three to four months I've been thinking of going.
"I've entered into Inter's history, I don't want to speak much because if I do, I'll cry and I don't want to do that.
"I want a different challenge in my career, now is the time to decide. What's important for Inter is that [president Massimo] Moratti and [captain Javier] Zanetti stay."
In all the post-match drama, it was easy to forget that Inter had become European champions for the first time in 45 years thanks to two goals from Argentina striker Diego Milito.
And the goalscoring hero hailed his coach as the mastermind behind the Italian side's Champions League victory.
"Mourinho deserves this the most. He is great coach and he deserves all of the credit for this success," the matchwinner stated.
"This is the team that he has made. He made many changes to the team that finished last year and we have come so far."
Milito was one of the players brought in by Mourinho last summer after Zlatan Ibrahimovic departed for Barcelona.
"I want to thank Inter, the president and the coach for wanting to sign me last summer - I am so happy to be here at Inter," Milito added.
"What I feel now is a joy I have never felt before, an incredible joy. I am so happy for Inter because we have been waiting for so long and we deserved this trophy."
Meanwhile, Inter president Massimo Moratti has revealed Mourinho cried after the side's victory, but hopes the coach was not shedding tears ahead of an imminent departure.
"I didn't cry, but Mourinho did and a lot - I hope they were not from a sense of guilt," Moratti said.
"The players were wrapped up in joy; it's an infinite joy, it's marvellous."
Source: BBC
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