Ranieri's side are in first place at Christmas just 12 months after being bottom of the table and the former Chelsea boss wants Leicester to maintain their pace at the top, likening their stamina to Tom Hanks' film character Forrest Gump, who ran across America.
"I am very confident because Leicester, last season, saved themselves in the last two months and that means the stamina is fantastic. Why can't we continue to run, run, run? We are like Forrest Gump" the colourful Italian said.
Ranieri cautious over Leicester's title chances
"The players know we are doing well but we haven't achieved anything.
"If I understand correctly, Leicester were never top of the league at this time so we are very happy. When the manager and the players make the fans happy then this is fantastic."
The Foxes, beaten just once this season, can cement their position as shock title challengers when they travel to Liverpool on Saturday and then host Manchester City on Tuesday.
From factory floor to record books for Leicester's Vardy
Leicester will beat Ranieri's pre-season points target of 40 with a win at Anfield and if they do that he will sit down with his players to re-evaluate their ambitions.
"I am very proud for my players and for my fans. It is fantastic but we have to work some more,"said Ranieri.
"Now they are dreaming and I don't want to wake them up."
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