A 1-0 win at relegated Siena on Sunday thanks to Diego Milito's second-half goal sealed their fifth straight scudetto and the second part of a potential treble on the final day of the league season.
NEWS:Nervy Inter seal Serie A title
The squad flew back to Milan after the game and appeared late at night in the city's main square on an open top bus, having earlier had to scrap plans for a party at the San Siro because of public order concerns.
Thousands of fans waved giant flags and set off flares in front of the city's giant cathedral, with several banners and chants asking Mourinho to stay after the Portuguese again said he is unhappy in Italy despite his success.
Media reports have linked him with a move to Real Madrid.
"It would be a great shame, I hope it doesn't happen," Inter chief executive Ernesto Paolillo told reporters.
"Now, however, let's think about his brilliance. After the Champions League final we will talk about what will happen."
Treble-chasing Inter, who also won the Italian Cup against title rivals AS Roma earlier this month, face Bayern Munich in Madrid on Saturday in their first European Cup final since 1972.
