The 25 year-old midfielder has impressed in the UEFA Champions League this season, scoring Shakhtar's winner in its last-16 first leg against Roma and reportedly drawing the attention of both Manchester clubs.
Palkan expects that Fred is destined for one of the two Premier League giants when the transfer window opens again later this year, with a €60million fee mooted.
"Fred will leave in July," Palkin said. "If he does not go to Manchester City, he will go to Manchester United.
"Fred is ready to play in the strongest league [in Europe]. He is not only a very good player but also a very good professional. I would like him to have one more year in our team, but he is ready for a stronger league."
The former Internacional star faced City in the UEFA Champions League group stages this season, playing the full 90 minutes in both a home win and an away defeat.
He made his international debut in 2014 and has been included in Tite's latest Brazil squad for friendlies against Russia and Germany, with the World Cup just three months away.