The 22-year-old completed a move to Chelsea on Sunday, with the Blues able to complete a deal that could reach £89million (four billion UAH) from under the noses of Arsenal.
Palkin explained he had met officials from the Gunners “three times”, but Chelsea were ultimately the only club that met the financial demands of the Ukrainian side.
Speaking to The Athletic, Palkin said: “Before Chelsea arrived, I did not know they were close, because I communicated with Arsenal in the same way as I had with Chelsea… I met Arsenal more times than Chelsea.
“Therefore, before this last meeting, Arsenal was close, or a little bit closer to this deal than Chelsea.”
He spoke of Arsenal’s lengthy attempts to convince the player, adding: “From my point of view, [this] is why everybody talked about Arsenal. It is because Arsenal contacted the player almost one and a half months before they contacted us.
“Can you imagine, for example, to have [Arsenal manager] Mikel Arteta, [Arsenal left-back and Ukraine international] Oleksandr Zinchenko and the sporting director [Edu] calling you, to have Arsenal calling you almost every day, every two days, every three days?
“If you talk about Chelsea, they called me at the end of December and asked if they can contact Mudryk because they are interested in him and want to talk with him. I said, ‘No problem, you can contact him’.
“The first time they contacted him was around the end of December or the start of January. They contacted the player and the agent of the player and they met the financial conditions.
“Why did many people around it have the impression that Mudryk was going to Arsenal? It is because Arsenal contacted him [first] and then Mudryk started to watch some games of Arsenal.
“But negotiations are negotiations. When you didn’t close everything, when you did not [close] the last dot, then you cannot finish the deal. It was just an outside visual impression that Mudryk [was] close to Arsenal.”
Palkin also confirmed Arsenal had also been willing to offer an overall figure of £89m, but that their final bid only included £62m up front, with £27m in add-ons.
“When we met Chelsea, we stayed all together,” he added. “For you to understand the context, it was for nine or 10 hours. They invited the player and explained to us the whole project.
“We realised that, yes, if you look right now, Chelsea have some kinds of problems but it is normal because they have a transition period from one owner to another. It is understandable.
“They would like to change a lot. So when they explain to you the whole story and you look for the next two, three, four, five years, then you see they have a serious project.
“I believe they will build one of the best clubs in the world because I am telling you, they are very serious in all directions: sports science, the stadium side, the commercial side, on all things. For us, they looked very ambitious.”