The Brazilian has been strongly linked with a switch to the Premier League in recent months with both Manchester clubs chasing him.
United were said to be considering a move for the 25-year-old in January before they signed Alexis Sanchez from Arsenal.
The 25-year-old came also close to joining neighbours City during a hectic transfer window but Pep Guardiola’s side had two bids rejected.
And Palkin has now dismissed there being an agreement for City to snap him him at the end of the season and has hinted a move to Old Trafford could be on the cards.
“Fred isn’t already at Manchester City, but he will surely leave in June — if not to City, then Manchester United,” he said.
“He’s ready for the next stage, because as well as being good, he’s also very professional. If he asked us to stay another year, we’d let him.”
Fred recently admitted he is hoping to leave the Ukrainian outfit having spent five years at the club, and is prepared to test himself in the Premier League.
“City are a great team, I would be happy to play there. Or at Manchester United as well… at Chelsea, Arsenal… clubs of great tradition in Europe and England,” he said.
“It is the best league in the world, I have no doubt, and I believe that my football would evolve.
“I’m 25. There’s a lot to grow and learn, play and observe great players of these clubs. That would help a lot — learn by watching them.
“I’m sure that I will evolve in the future and that my agents will help me a lot to make the best decision possible, so that in the next window I am at a Premier League club.”
Fred, who is under contract with Shakhtar until 2023, is rated at around £40m.