According to David McDonnell of the Daily Mirror, the Red Devils are intent on landing the Italy international ahead of their neighbours despite the fact the player's representatives have already held talks with City.
"He heads Mourinho's midfield wishlist, with Nice's Jean Michael Seri and Shakhtar Donetsk's Fred also on his and City's radar," read the report. "But United will have to fight hard if they are to land Jorginho. City have held already outline talks with his representatives over a summer move to the newly-crowned Premier League champions."
It's also noted Napoli value the playmaker at around £50 million. McDonnell said United want to bring in two midfielders this summer, with Marouane Fellaini set to leave the club and Michael Carrick retiring.
Jorginho has been impressive for the Serie A giants this season, as he's helped the team rival Juventus in the title race. Napoli trail the Bianconeri by just one point with four games remaining in the campaign.
The possession-based, attacking football Maurizio Sarri utilises is dependant on Jorginho. As noted by ReviewFootball, in Napoli's recent win against Juve, the deep-sitting midfielder was the dominant force at the hub of the team:
While Jorginho isn't a classic shielding presence in front of the back four, he often puts his stamp on games.
The Brazilian's biggest strength is his ability on the ball. When opponents push up against Napoli, he can drop pinpoint passes over the top of the defence for forwards to run on to; if they sit deep, he can dissect a defence with delicate balls between the lines.
With that in mind, it's easy to see why a team like City, who are stylistically similar in some ways to Sarri's side, would want to secure a player of Jorginho's ilk. But for United, who don't tend to pass the ball through the phases consistently under Mourinho, his fit would be a little more curious.
Bleacher Report's Sam Tighe doesn't believe Mourinho would be the right type of manager for the Brazil-born playmaker:
But Sam Lee of Goal said City are confident of getting their man at the end of the Serie A season:
Jorginho would bring variety to United in midfield and would be a fine complement for someone like Paul Pogba. He'd also be a big asset for Mourinho when teams seek to stifle and frustrate the Red Devils, as allowing the Italian time and space on the ball is dangerous.
Even so, for a player like Jorginho, a switch to City would surely be more appealing. Guardiola would bring the best out of his style, and given Fernandinho is the only other midfielder in the squad comfortable playing in front of the back four, the Napoli man would get plenty of game time at the Etihad Stadium.