Tuesday's 2-0 win over Liverpool, courtesy of Jamie Vardy's brace, puts Leicester three points clear at the summit ahead of trips to traditional heavyweights Manchester City and Arsenal in the next fortnight.
The outcome of their visits to the Etihad and Emirates Stadiums could make or break Leicester's chances and Ranieri says his side - who battled relegation for long spells last term - remain unfancied for the title.
Referencing Barack Obama's slogan during his successful run for the United States presidency, the Italian told reporters: "I'd like to say 'Yes we can!', but I am not Obama. If I maintain this suspense it is much better.
"Of course we are underdogs. Even if [the other teams] push a little more and accelerate they go. We have to run a lot.
"Calm. Calm. Calm. Our fans must dream. We must stay with our feet on the ground. If we arrive fourth and go in the Champions League, unbelievable.
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"During the pre-season friendlies, I believed in these players and I gave them all my confidence and support. Never did I blame them and say: 'We conceded this goal because you did this or this.' No. I said: 'Okay, we replay the highlights and we try to improve.'
"I want the intelligent man. If you have intelligent men, you can improve the player. You can be a fantastic player but if you're a stupid man you cannot improve. I have very intelligent players."
Vardy has arguably been the star of the show for Ranieri's side, with a stunning long-range opener against Liverpool helping him top the Premier League goalscoring charts by three from Tottenham's Harry Kane.
The 29-year-old's contract expires in 2018 but the England international had reassuring words for Leicester fans.
"It will be sorted. I am leaving that to my agent," Vardy said.