The Algeria international won the PFA Player of the Year award this season after scoring 18 times to help fire the Foxes to an improbable title.
They will receive the Premier League trophy after tomorrow’s final home game of the season against Everton.
Mahrez signed a new four-year deal last year but has been linked with a move away, with Barcelona reportedly interested, although Ranieri believes he will keep him.
“It’s 99% he will stay,” Ranieri said. “I’m very, very confident. I suggest to all my players stay one year more. Don’t go. If you go (to) another team, you might not get on the pitch.”
Leicester’s vice-chairman Aiyawatt Srivaddhanaprabha revealed last night that Mahrez has told him he wants to stay.
Ranieri gave the players an extra day off this week but insisted he expects total professionalism tomorrow and warned them there will be consequences if they fail to meet his demands.
“I kill them, with my bare hands,” he joked. “It is important to clean our minds and keep going with our jobs. This is very sweet but our job is to play.
“Of course there will be a good match for us, now we are champions but Everton want to beat us so it is right to put our mind on the job. I’ve watched how they train and it was good.”
The city has been celebrating since winning the title on Monday, following Tottenham’s 2-2 draw at Chelsea left the team seven points clear with two games left.
And Ranieri admitted he wants to sneak into the city and see the party.
“I’d like to go around the city with black glasses to watch what is happening — it’s amazing,” he added.
“It’s difficult to give a message to these fantastic people. They were dreaming, I say ‘dilly ding, dilly dong’, they wake up and the dream is a reality. I can only say thank you with all my heart.”
Meanwhile Robert Huth and Marouane Fellaini have both been banned for three matches for violent conduct.
The pair were charged by the Football Association following their off-the-ball clash in Manchester United’s 1-1 draw with Leicester on Sunday.
Huth was caught by TV cameras pulling Fellaini’s hair, with the United midfielder responding by swinging an elbow into Huth’s neck.
An FA statement said: “Both players accepted the charge, however, Huth contested that the standard penalty of a three-match suspension would be ‘clearly excessive’.
“This claim, however, was rejected following an Independent Regulatory Commission hearing today.”
The incident was not seen by the match officials but a panel of former referees agreed both offences warranted red cards.
Huth will miss Everton’s visit tomorrow and the Foxes’ final match against Chelsea as well as next season’s league opener.
Fellaini, meanwhile, must sit out United’s last three Premier League games but will be available for the FA Cup final against Crystal Palace.
Louis van Gaal reiterated his stance that United should have had a penalty for Huth’s offence but accepted Fellaini should not have reacted in the manner he did.
The United boss said: “When the FA give Huth a suspension of three matches, then they admit it was a penalty. I said that also after the match.
“For us it is very disappointing that the referee was not seeing the fact. I think and still believe that Fellaini makes a reaction like a human being but he has to control himself better, that is true.
“When you grab somebody in his hair, always this situation shall exist.”