The 67-year-old said that he has had a number of clashes with the Welshman regarding the issue and will never change his opinion.
He also revealed a list of current Premier League stars that he suggested the Potters should recruit before they secured moves elsewhere.
"We have loads of disagreements, because I don't like the way they play and I will never change on that," Parsons told The Sentinel. "I have been told that players I've recommended have been too small for Stoke, but I don't go along with that. Look at Lionel Messi, he is different class and is he too small?
"I have recommended players like [Cheick] Tiote, [Hatem] Ben Arfa and [Demba] Ba, but they have not been signed by Stoke and they have done well for other clubs.
"I remember one of the first names I gave to Tony at Stoke was a lightning-quick, 6'4" striker called [Emmanuel] Adebayor, but we were in the Championship and we were told the fee of £3m was too much."
Stoke are currently hovering in 13th place, just four points above the drop zone.