The Portuguese was axed by United on Monday after 18 months in charge.
Among the names being mentioned as a successor is Enzo Maresca, who quit Chelsea on Thursday.
With United chiefs Omar Berrada and Jason Wilcox having been at Manchester City when Maresca was working as a coach there, the connection is driving major speculation.
However, Butt said on the The Good, The Bad and The Football podcast: "If Maresca comes in - I like him as a coach, I really do - with the background, I would give my season tickets back.
"I can't sit here and go on about Man united philosophy and DNA and then go, 'Well I'd love Maresca', an ex-Man City guy. Then you have Omar Berrarda and Jason Wilcox.
"I don't care how much success is. You're forgetting where I'm from. Everyone is a City fan. I'm a Man United fan and I can't accept that."