The sacked Manchester United boss is still adored by Inter fans having delivered the treble in 2010.
Mourinho was fired by United on December 18 and is looking at his route back into management, holding talks with Inter on Thursday, according to the reports in England.
He has already turned down the chance to take over Benfica and is understood to be content with assessing his options until the summer.
Antonio Conte is also a potential candidate with current boss Luciano Spalletti under mounting pressure.
Inter are third in the Italian top flight but remain a massive 20 points adrift of leaders Juventus.
There is a feeling that Mourinho could help close that gap, one echoed by former Inter chairman Massimo Moratti.
‘Would I like Mourinho back at Inter? Yes, I’m very fond of him,’ he said.
‘However, we’ll give time to Spalletti to prove his worth. Diego Simeone? I love him too, but Mou is special.’