Mourinho, 47, is now expected to become Real Madrid boss after guiding Italian domestic Double winners Inter to an historic Treble thanks to a 2-0 win over Bayern Munich in Saturday's Champions League final at Real's Bernabeu stadium.
After the victory over the German champions, former Chelsea and Porto boss Mourinho said he was keen to move to Real, who are currently managed by Manuel Pellegrini.
On Monday, though, Mourinho dodged questions about his future following the meeting with Moratti, saying: "The only thing that I can say is that I have enjoyed very much eating with my president. You always eat well at Moratti's house."
Mourinho's agent Jorge Mendes held a 90-minute meeting with Real Madrid director general Jorge Valdano and sporting director Miguel Pardeza on Monday, according to Spanish media.
Spanish newspapers AS and Marca have reported that Mourinho will sign a four-year deal with Real worth £8.5m annually, though Inter want £13.7m in compensation as the Portuguese's contract with the Serie A side runs until 2012.
Later on Monday, Sinisa Mihajlovic quit as Catania coach, amid speculation that the Serbian, who departed as Inter assistant coach in 2008, is set to succeed Mourinho at the San Siro.
"I hope to soon find a job which legitimises my decision and my professional ambitions," Mihajlovic told Catania's official website.
By winning the Champions League, Mourinho became only the third coach to win Europe's top prize with two clubs.
"I'm so sad as almost for sure it's my last game with Inter," stated Mourinho after the Nerazzurri beat Bayern Munich in Madrid. "If you don't coach Real Madrid then you always have a gap in your career."
He continued: "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.
I didn't cry, but Mourinho did and a lot - I hope they were not from a sense of guilt
Inter president Massimo Moratti
"Everybody knows that English football is my passion and I will go back to England."
Mourinho, who joined Inter in 2008, has also won two Serie A titles as well as the 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 said.
"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."
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