"He told me that he wanted to stay with us," Palotta told radio station SiriusXM.
"I'll say more, I was surprised by the fact some of the players I thought had wanted to leave came up to me before and after the final game to say they wanted to remain.
"It's a sign we've got a good group, we just lack some depth and Monchi (director of football) will help us with that."
Media reports have linked Szczesny with a switch to Serie A champions Juventus with the final decision about the keeper's future resting with Arsenal.
(Reporting by Aditi Prakash in Bengaluru)
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