Brazil international midfielder Fred has been tipped to join either United or City in the close-season, having impressed domestically and in Europe this term.
Goal understands City agreed a deal in principle to sign him from Shakhtar this summer, while the Ukrainian side's chief executive Sergei Palkin has said the Manchester rivals will battle for the 25-year-old, who is in Brazil's 23-man squad for the World Cup in Russia.
While he is happy at Shakhtar, former Internacional star Fred feels ready for a challenge elsewhere in Europe.
"I'm very happy at Shakhtar," Fred told SporTV. "I've been working well here but it has been five years.
"I made it clear to the club that I was very happy here but I want to make a bigger leap in my career.
"Now I just have to wait to get through the World Cup and see which is the best destination.
"I think I have to change a little. I have dreams of playing in major clubs in Europe. I made it clear that it's my moment.
"The club are reluctant to release [me]. I have a contract until 2021. As soon as I come back from the World Cup we will sit down, talk and look at the options."
Fred, who joined Shakhtar in 2013, has scored four goals in 37 appearances in all competitions this term.