Moratti invited Mourinho to his house in the heart of Milan for dinner on Monday night in a final attempt to persuade him to stay for a third season at Inter but Real Madrid appears to be the Portuguese coach's next stop.
When asked if Mourinho's working relationship with Inter could be considered to be over, Moratti said after the meeting with his coach: "I believe so. The approach of the coach is that of someone who is already thinking of going to Real Madrid."
Indeed, Mourinho admitted after Saturday's Champions League final win over Bayern Munich at the Bernabeu Stadium that he was keen to replace Real coach Manuel Pellegrini.
Mourinho led Inter to arguably the best season in club history with a Coppa Italia, Serie A and Champions League treble.
He has a get-out clause in his contract, provided a fee of 16million euros is paid.
Mourinho dodged questions about his future and briefly said after the dinner: "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."
Several coaches have been linked with Inter as a replacement for Mourinho.
Former assistant Sinisa Mihajlovic, an ex-defender at Inter, has been mentioned in the Italian press as a candidate have announced his departure from Catania on Monday night.