The Manchester Evening News is reporting that the Portuguese coach is pondering a move to sign the Italy international this summer as he bids to bolster his squad ahead of next season.
The same story says that Mourinho has spent the last nine months drawing up a transfer wishlist ahead of the summer window.
According to the same article, Verratti is one of a number of big-name transfer targets being considered by Manchester United this summer.
The article says that Mourinho watched Verratti in action during Italy’s World Cup playoff defeat to Sweden at the Friends Arena in Stockholm last year.
And the Red Devils are now said to be considering a bid in the region of £75m-100m to bring the 25-year-old to Old Trafford this summer.
Manchester United ended last season without a trophy, as the Red Devils missed out on the FA Cup following their final defeat by Chelsea FC at Wembley.
The Red Devils finished second in the Premier League and 19 points behind champions Manchester City.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news