The Millers are gunning for a third successive rise from League One having yo-yoed between the third tier and the Championship over the last six seasons.
They have endured a solid, if not spectacular start to the campaign, having taken nine points from their opening five games.
Now that the transfer window has shut and they were able to add Will Grigg to their ranks while also keeping key players, Warne thinks he has a squad capable of challenging the likes of Sunderland, Sheffield Wednesday, Wigan and Portsmouth.
He said: “Yes, I do. I don’t know if that is putting pressure on myself or my players, I hope it doesn’t.
“But I have said it to their faces and am happy to put it out there.
“We have got a really good squad. Having a good team is one thing, but whereas good teams win games, good squads win promotion, really.
“You need strength in depth, which I think we have got. However, you do need form, luck and a lot of things.
“But I do think we have ticked a lot of boxes with our squad. Everyone bandies the word ‘culture’ about all the time, but I do think we have a good environment.
“I am not naive and being disingenuous. I do think we have got a good team full of good players and with a good run of luck, we could be there or thereabouts. But if we are not, then we are not and that comes on me.”
The Millers resume their League One campaign against Fleetwood on Saturday.
They were not in action last weekend after their game at Lincoln was postponed due to international call-ups.
They visit Sincil Bank on Tuesday for the rearranged tie.