However, in an interview with Correio da Manha (h/t Football Espana) on Thursday, he ruled himself out of a return to Benfica after being heavily linked with the vacant position at the Estadio da Luz following the departure of Rui Vitoria:
"Today I have no intention of returning to Portugal. Benfica aren't an option for me today. [Returning to Madrid or Inter would be] a huge honour, but I'm talking to you and no-one else right now. When a coach or player returns to a club, it means they did something positive. That's how I felt when I went back to Chelsea.
"When a professional returns or is invited to return to a club, it's a great honour. If you're asked back, it's because they know your worth. Now I have the right to relax, wait, have time to critique myself and analyse everything I've gone through in the last few years with calmness, to be able to think and prepare for the next phase of my career."
Mourinho, 55, endured a disappointing two-and-a-half-year spell at United before being dismissed.
He won a UEFA Europa League and League Cup double in 2016-17, his first campaign with the Red Devils, but he failed to launch any kind of Premier League title challenge and installed a dull brand of football at the club.
The Portuguese manager also created a bad atmosphere at United, falling out with a number of players, including club-record signing Paul Pogba:
Mourinho's spell in Manchester has done little to enhance his reputation.
He left Real on relatively good terms in 2013, though, and he remains a legend at Inter after leading them to treble glory in 2009-10.
Luciano Spalletti is currently in charge at the San Siro, with Santiago Solari the boss at the Santiago Bernabeu.
Neither is completely secure in their position, as both clubs are effectively already out of their respective league title races, and Real are even struggling to make the top four in La Liga and qualification for next season's UEFA Champions League.
It is not particularly hard to imagine one of Spalletti or Solari losing their job at some point in 2019, and Mourinho would immediately be a strong favourite to replace them.
He is clearly open to the prospect of returning to Inter or Real, and he can point to successful stints at both clubs.
Mourinho's second spell in charge of Chelsea did not end well, but before he was sacked by the west London club in December 2015, he was able to deliver them the 2014-15 Premier League title.