Manchester United want Fred to bolster their midfield and help give more freedom to Paul Pogba to work his magic further up the pitch.
Shakhtar - who have specialised in taking and developing elite talents from Brazilian football before selling them on to Europe's most moneyed clubs - signed Fred from Internacional in 2013 for a transfer fee of €15m.
Fred, 25, was City's main midfield target in January and moves were made to strike a deal before Shakhtar chose to hold on to the all-action Brazilian until the end of the Ukrainian season. "I've been working well here but it has been five years".
The midfielder admits there's interest in him from France and England and he insists it would be a dream of playing for a "major" club in Europe.
'I made it clear to the club that I was very happy here but I want to make a bigger leap in my career. I want to make a bigger leap, I made it clear to the club.
'The club are reluctant to release [me]. "And of course, some of the players I am totally convinced are going to make it, some others I have good hopes that they are going to make it, and some others I don't believe they are going to make it".
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"How many points separate us from Manchester City?" said Mourinho last week. I have a contract until 2021.
Manchester City are also keen on the 25-year-old.
Fred is tied down at Shakhtar until 2023 having extended his contract in January this year.
And according to M.E.N's Samuel Luckhurst, United also face competition for Fred, whose release clause stands at €60m (£52.89m), from PSG ahead of Thiago Motta's departure from the club.
While a potential move to join compatriots Neymar and Marquinhos at Paris Saint-Germain has been touted as well.