The Lancashire side exceeded expectations last term in finishing seventh and securing a European spot.
However, Dyche remains pragmatic over how far Burnley can progress beyond last season's exploits, though he admits that "the possibilities are endless" given Leicester City's title triumph in 2015-16.
"It might well be seventh is the highest Burnley can ever finish, we don't know yet," Dyche told The Telegraph. "Seventh isn't the highest 'possible', it might be the highest 'probable'. The possibilities are endless, we all saw that when Leicester blew the roof off.
"Probably, it is difficult to go beyond seventh in this division when you are us. And a number of other clubs could say the same. Because the top six are that powerful, I think. But you never know. When I came here none of this was envisaged.
"Staying in the Premier League is a start point because that's the minimum objective you want to get to – beyond that who knows? The challenge we are trying to cement is being a recognised Premier League team. That's the challenge. Anything beyond that is either a good season or a bad season.
"'Recognised' is year on year on year, when people just get used to you being in there. We're not there yet. There are a handful of clubs who are not there yet. Very few clubs outside the top six have got a gimme. That's not being negative, that's just the reality of us in this division."
Burnley take on Aberdeen in the Europa League second qualifying round, the first leg taking place at Pittodrie on Thursday.