The recently axed Manchester United manager spent two seasons in Serie A with the club, winning the league in his first season and a historic treble in the second before moving on to Real Madrid.
With a win ratio of 62%, the highest within his glittering managerial career, the Portuguese tactician is said to be keen on a second stint in Italy.
With Inter last winning the league title under his guidance nearly a decade ago, Mourinho, 56, has already instructed his agent Jorge Mendes to contact Inter Milan CEO Beppe Marotta and director Piero Ausilio according to Libero.
Current manager Luciano Spalletti's future is far from assured with the Nerazzurri with Inter 20 points behind Serie A leaders Juventus, but Marotta has confirmed the forthcoming game against Parma will not make or break his future.
"It is absolutely not true that the Parma game is decisive for Spalletti. We recognise that this is a difficult moment for Inter.
"We are in a transitional period of the season, as there are 16 matches to go and we are in third place. It’s true, our form has been going down lately, but we can count on a strong club, a competitive squad and a coach who is very capable. We'll emerge from it stronger," Marotta told Sky Sport Italia.
In the off-season, Spalletti signed a new contract to keep him at the club until 2021, but his future may well be revisited in the summer, and Libero claim the Nerazzurri management are already thinking about a new coach for the next season.
The report claims former Chelsea man Antonio Conte remains Marotta's first choice, but Mourinho's name cannot be excluded with possible negotiations between Inter and Mourinho's delegation set to start this month.