Puel is the bookmakers favourite to be the first manager sacked in the Premier League this season, though his side looked impressive in their opening game against Manchester United.
Before his side's second match against Wolves on Saturday, the Frenchman has claimed: "It's just speculation. I would be happy for my successor, because he would have a good squad and a very good team.
"I can't comment on speculation. I don't bet and I don't do the lottery - it's not my way.
"My job is to build something with Leicester; to continue to develop this club, to develop the players and the squad. After this, if people are angry or not satisfied, that is my concern.
"It is not the first time, it will not be the last."
The 'Foxes' are reportedly aiming for European football this season, having finished seven points off Burnley last season who are currently competing in the Europa League.