Leicester, 5,000-1 outsiders at the start of the campaign after narrowly escaping relegation last term, are seven points clear at the top of the table with six games left, and within touching distance of their first top-flight crown.
"They've been incredible," Cottee told Reuters in an interview.
"When you look back to this time last season, they looked doomed to get relegated. I think they won seven out of their last nine games to stay in the Premier League."
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Identifying the risk that Leicester took by bringing in manager Claudio Ranieri after parting ways with Nigel Pearson, Cottee praised the Italian for the ethos he had instilled at the club.
"I like Ranieri's approach," Cottee added. "He's very calm, he's very relaxed, he looks like he's enjoying it, and that's infectious. It rubs off on the players.
"If you've got a manager who's all uptight and angry about everything it can get you down a little bit.
"There's a lot to be said for having a good team spirit and a happy camp and if you're enjoying your football, you just go out and play your natural game."
Leicester's relatively injury-free campaign had allowed Ranieri to identify his strongest team early in the season, while not being involved in Europe gave them an advantage over big teams, such as Chelsea, Manchester United and Liverpool, that have underperformed this season, Cottee said.
A strong defence, augmented by the talent of Riyad Mahrez and N'Golo Kante, and the confidence of Vardy, had made Leicester favourites to win the title, he added.
"I'm not very happy with Jamie because he broke my Leicester goalscoring record this season," Cottee joked. "But congratulations to him, he's been absolutely fantastic.
"It's for Leicester to lose this particular league title and the only thing that will make them lose it is the pressure.
"But it's in their own hands, they're in a fantastic position and unless you're an Arsenal or a Tottenham fan, everyone in the country, probably everyone in the world, wants Leicester to win it.
"If they were to win the Premier League it would be the greatest achievement of the modern era, certainly in terms of the Premier League."
(Editing by Tony Jimenez)
