The 56-year-old Frenchman -- who was fired by Southampton at the end of the 2016/17 campaign despite reaching the League Cup final and finishing eighth in the table -- says he did not come in to replace Craig Shakespeare last October just to save the club's place among the elite and then leave.
Puel -- who tasted success early in his coaching career when he led Monaco to the 2000 French Ligue 1 title -- has seen his position come under fierce scrutiny from fans with just five wins in their last 20.
However, he will still be only the second coach of The Foxes this century to guide them to a top 10 Premier League finish -- Italian Claudio Ranieri's title win being the other one.
"We will see if it is possible or not but I have a good feeling because it is the most important thing for the club," said the 56-year-old, whose side finish their campaign against Tottenham Hotspur on Sunday.
"I didn't come here just for some games and to try to save the club. I want the project, I want to work to develop the play and the squad.
"For example, we have finished ninth or maybe eighth but we have finished in the top 10 only two times for 18 years."
Puel, who received the backing of Thai owners chairman Vichai Srivaddhanaprabha and his son Top after a meeting earlier this week, said it was crucial to give a decent run to the manager to allow the club to progress on the pitch.
"This is a fact. This club needs consistency and to develop something strong, with solidity and strength," he said.
"This needs time and we need also to work hard in the summer in the transfer window.
"We need to improve this team and develop some good players also. We will see the results next season.
"It is important to understand this and to have a good consistency in our work during the difficulties.
"A manager needs to keep the way in all conditions."
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