RAI Sport says talks have started to get the holding midfielder at Old Trafford for the start of next season.
Members of Jorginho's entourage met with senior United officials about a proposed move in the summer.
Jorginho is seen at Old Trafford as a replacement for veteran captain Michael Carrick.
The midfielder will retire at the end of the season and with Marouane Fellaini's future very much up in the air Mourinho is on the look out for reinforcements in the middle.
Jorginho has been monitored along with Borussia Dortmund duo Julian Weigl and Christian Pulisic and has already impressed when playing against Manchester City in the Champions League earlier this season.