Warnock's Leeds, who have struggled to mount a serious promotion challenge, have saved their best form for the cup competitions this season and have already beaten Southampton and Everton in the League Cup and latterly Tottenham in the FA Cup to set up an intriguing fifth round clash at the Etihad Stadium.
"According to the bookies we're at 33-2 in a two-horse race," said the 64-year-old.
"I don't think many people are going to put any money on us.
"But the FA Cup is such isn't it? It's such a great competition. It would be a major upset if we went there and won, but we're looking forward to it.
"I don't think many people, when the team sheets came out, gave us much chance against Tottenham or Everton, but it's a little bit more difficult with it being at the Etihad as well.
"They'll be right up for it and I would imagine they'll want to try and win the tie early doors so they can relax and enjoy themselves."
Warnock has taken some stick from Leeds fans in recent weeks and one point gained from their last three league games has left them eight points adrift of the play-offs.
"We've done brilliant in the cups this year, I don't think anyone's done better than us," Warnock said.
"Everton played a strong team, Tottenham played a strong team and we did well against Chelsea for 45 minutes.
"We've had a very good run and it's shown what ability we've got in the squad.
"That's what makes it more frustrating in the league. But this is by far the toughest one. They're champions of the Premier League, we're away from home and it's the only competition they've got left to win. It's difficult.
"But we're going to enjoy it. There are no league points at stake and I'm sure the fans will enjoy going over there."
Manchester City boss Roberto Mancini is also feeling the heat after watching his side's chances of defending their Barclays Premier League title all but ended last week when defeat at Southampton left them 12 points behind rivals Manchester United.
"When you're at a club like that and you've spent what they've spent you're always going to get pressure," Warnock said.
"The pressure is that they're only second in the league. But that's what you get with the job, I think every manager would like those pressures to be able to go and buy anybody you want in the world.
"It made me laugh when Roberto said he was going to drop some players, what he meant was he's going to bring the first-teamers who weren't playing last week back in, like Kompany and Tevez. When you look at the squad it's fabulous."
Warnock, who said he has buried the hatchet with Carlos Tevez following the infamous incident involving West Ham when he was manager at Sheffield United six years ago, senses a high-profile cup tie can bring the best out of his players again.
"We've got some good players. We've got players who have shown if they all do it together at the same time we can give anyone a good run for their money.
"We've got young players I believe could play in the Premier League, three or four, we've got one or two old campaigners who love the atmosphere and what the Etihad will bring and I'm sure with television being there as well they'll want to perform.
"So if all the pieces fit on the day there's no reason why we can't give them a good game and that's what we want to do.
"We want to go there with a big following and give them a good game."
Warnock got the better of City the last time he crossed them in the FA Cup, as manager of Notts County in 1991.
"They were a top-flight team and Peter Reid was moaning because there was snow on the pitch, so it is possible, but tougher now. Away from home against a top side.
"But it's a two-horse race and hopefully one or two of them might have been out on the town the night before."