The Blades have been impressive on their return to the Premier League, while fierce rivals Sheffield Wednesday are battling in the Championship.
"I see more and more Sheffield United shirts around town," the Blades boss said in an interview with Sky Sports.
"We've got a fantastic opportunity, if the club gets it right, to rule the city for the next twenty, thirty years.
"We want to dominate this city because that's how we are - and the other lot are exactly the same. They might not say it - and they might say, 'Oh, he's talking about us again' - but that's how it is.
"We want to be an established Premier League club, we want to dominate the city, we want Sheffield United shirts all around, we want 30,000 at every game."