The 19-year-old, who plays for MTK, spent a week in south Wales and was happy with how things went.
"They said they had been satisfied with me and were hopeful to meet me again. I hope so too," Baki told Nemzeti Sport.
"I was with the Under-21 team of Swansea except when they had a game - that time I was training with the Under-18 team.
"I had an extremely tough weak. The conditions are very different (to the Hungarian conditions), for example, Swansea have two training centres.
"The players' mentality is really different, everyone wants to be a footballer and you really feel it.
"Everybody speaks and communicates on the pitch and they don't say a bad word if you make a mistake but encourage you. The speed of the game is high and the players are faster and also physically and mentally stronger.
"What's more everyone was very kind, they treated me as their team member from the first minute. To sum up, I felt great."
Baki's agent is hopeful a deal could be done. Ferenc Fulop told NSO: "According to the reflections it seems that they liked Baki's performance.
"We're waiting for the club's official response, it'll be decided within a couple of days if they make an offer for the player to MTK or not."