Mourinho is eager to beef up his midfield with Michael Carrick retiring and Marouane Fellaini widely expected to leave on a free.
A deal for Fred appears to be in the pipeline and a move could cost as much as £52.2million once add-ons are taken into consideration.
As far as Verratti is concerned, reports have suggested United are lining up a bid worth £100million.
The Italian has been linked with a move to Manchester United in the past and it is suggested Mourinho wants to make him his marquee signing.
Further reports have indicated that West Ham could be left disappointed with new boss Manuel Pellegrini harbouring ambitions of signing the 25-year-old.
Mourinho is expected to be heavily bankrolled this summer to close the gap to Premier League champions Manchester City.
And according to The Sun on Sunday, United are adamant they need two central midfielders.
It is suggested that Mourinho wants to make Verratti his next signing after Fred has arrived.
Barcelona legend Xavi admitted earlier this year he sees a lot of similarities between himself and Verratti.
He said: “I would say that in today’s football, the one that resembles me the most is Verratti.
“Technically, he has everything, he does not lose the ball, he is able to make the pass.”