Blackburn Rovers were the last side outside those clubs to win the league title, in 1995, but Spurs can move level on points with the leaders Manchester City if they overcome McCarthy's Wolverhampton Wanderers at White Hart Lane.
McCarthy said: "Spurs are genuine title contenders. People say it's all about 'can you believe you can win it' when you get to the last six games.
"But they've got great players and I'm sure Harry Redknapp will be trying to add to that this window, also keeping everyone fit and making sure they all stay on the pitch.
"If they do, then, yes, they are a genuine contender for the title and it would be refreshing for someone else to win it … they are a fantastic side and as good as anyone in the top three or four."
McCarthy, the former Ireland manager, added that he believes Redknapp, his Spurs counterpart, would be ideally suited to replace Fabio Capello as England's coach after Euro 2012.
He said: "With the experience and wisdom of someone that has been a top manager for so long, Harry is more than well equipped to do it."
McCarthy's side start today just one point above the relegation zone. He said he is ready for another relegation scrap and agrees with comments by the club's owner Steve Morgan that results were below expectations during the first half of the campaign.
"Let me clear something up. I think the results have been unacceptable. I think it is unacceptable where we are," he said. "I don't think we should be where we are. I think we should have more points. As for anyone else's opinion, they are only agreeing with me."
He added: "We took 22 points from 19 games in the second half of last season to take us to 40. Will that be enough, or what's the magic tally, I don't know.
"To beat that, to get 24 points, to get to 41, everyone is going to have to take eight points from every six games. That would be some tally for anyone in the bottom half of the table to be getting that."
Meanwhile, Redknapp yesterday insisted that the midfielder Steven Pienaar will not be leaving the club, amid reports of a bid from Queens Park Rangers to lure the South Africa international across London.
Pienaar has failed to establish himself under Redknapp since moving from Everton a year ago, but the Spurs manager said: "I wouldn't want to let him go. He is a good player."