Former Arsenal midfielder Paul Merson said on Saturday that Dyche, who has twice taken Burnley into the Premier League, should be among those considered for the top job at the Emirates were Wenger to leave at the end of the season.
Wenger’s future remains undecided, though the Frenchman has made clear that he wants to extend his contract beyond the season’s end, but Dyche cannot envisage himself being among the contenders when the Arsenal vacancy eventually emerges.
“I think it's highly unlikely that English managers are getting massive jobs in the Premier League, at the moment,” Dyche said.
“Maybe over time the feeling about football changes. I just don't think English managers have still got the kudos of some of their foreign counterparts. That's not a big deal, that's the nature of what it is at the moment.
“I think for Arsenal I need some more experience, more depth to my experience, more growth as a manager and I think it's fair to say that we're working hard at what we do here.”
Dyche is one of six English managers currently in the Premier League, none of whom are in the top half.
Though Bournemouth boss Eddie Howe has at past been linked to the Arsenal job few English managers have been given chances at the likes of Chelsea and Manchester City.
“I just don't think they're thought of in the same way sometimes as what their foreign counterparts are,” Dyche added. “There's no angle in that, I just think it's the reality of where it's at.
“Arsenal have got a top-class manager, they've got one already and if anyone wants him out they'll probably look and say ‘shall we get the same version of him in?’ I think he's top class personally.”