Fred was one of Shakhtar's best players in the 2017-18 season as they picked up another Ukrainian league title.
But that has not deterred his suitors with many clubs keen on the versatile midfielder and Mourinho may want to get in before the rest to secure the signing.
The deal could be completed ahead of the World Cup, as Fred will travel to England next week for Brazil's friendly with Croatia at Anfield, which gives him the opportunity to put pen to paper on a contract at Old Trafford.
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As a result, Manchester United are expected to try and get the transfer over the line in the coming week, when Fred will be travelling to Anfield, which is just 29 miles from the Red Devils' Carrington training complex, for an worldwide friendly against Croatia.
Twitter user Jonathon posted a clip showing him searching for Fred's name in Norwood's list of people following.
Fred is an excellent technical player, coupling his passing range with a high intensity work-rate, great balance, composure, and a delightful dribbling ability even in the face of intense pressing. United are in desperate need of a midfielder with good ball-winning qualities as well as a desire to push forward, so should he join, Fred could prove the flawless foil for Nemanja Matic and Paul Pogba. That is, I can somewhat feel that Fred will be more expensive than Fernandinho and Teixeira.
Manchester United are expected to spend big this summer as they aim to close the gap on rivals Manchester City.
Brazil midfielder Fred claims transfer talks with Manchester United is at an "advanced stage" and explained why both Jose Mourinho and Pep Guardiola have been interested in his services.