City remain favourites to sign the 25-year-old, but Palkin has suggested that United are still competitive in the race to secure the player's services at the end of the campaign.
Palkin told Corriere dello Sport: "Fred will leave in June. If not to Manchester City, then to Manchester United.
"He is ready for the best championships. 'In addition to being very good, Fred is very professional."
Fred has impressed in this season's Champions League, with a goal coming in the 2-1 win over Roma in the first leg of the last-16 tie between the two clubs.