Chelsea sacked Mourinho in December 2015 following a disastrous defence of the club's Premier League title, with players such as Eden Hazard publically declaring their admiration for how new coach Antonio Conte has changed the atmosphere at Stamford Bridge.
Mourinho was hired by United last summer following Louis van Gaal's sacking, and has led the club to an EFL Cup triumph despite a rocky start to life at Old Trafford.
The Portuguese coach has admonished the likes of Henrikh Mkhitaryan, Anthony Martial and Luke Shaw as he seeks to drive his side on, with Mesut Ozil recently revealing that the former Real Madrid boss called him a "coward" during their time together at the Bernabeu.
United can go fourth - albeit temporarily - if they win Saturday's early kick-off against Bournemouth, and the Guardian reports Mourinho as saying: "I think Manchester United learn I am not the monster that you [some sections of media] say I am.
"I’m not such a bad guy, an arrogant guy, a different person to work with.
"At least until now nobody at the training ground runs away when I arrive.
"So people are quite happy to have me around and to work with me, the relation with the players is very good and with my owners and my board the relation I don’t think is just professional; it’s also a relation of trust and a relation that goes further than the contract, the manager, the owner, the board.
"I’m happy. My feeling is everyone is happy but obviously my contract is three years, not seven or eight months and I want evolution and improvement."
Mourinho's confrontational approach to bringing out the best in his players has seen both Mkhitaryan and Martial restored to first-team roles after the attacking duo spent spells on the sidelines.
Left-back Shaw has struggled to impress Mourinho this season, but the coach says the young defender has a crucial chance to make a statement against Bournemouth.
"Luke Shaw, I have good news for you," Mourinho said.
"He is selected for tomorrow so you won't need to have the guys at The Lowry to take pictures of who is selected and make the list.
"He's in the list for tomorrow, so one step up from not being selected, not being in the final even on the bench.
"Like Wayne he's selected, so playing or being on the bench, he becomes again an option to us.
"Luke is working hard, he's trying to improve.
"He improved by the physical point of view, I can say, for sure, with good dedication, good specific work and now obviously he needs some opportunities to feel alive, he needs opportunities to play."
Additional reporting by the Press Association.