While a seven-point lead over second-placed Tottenham is not enough to persuade Ranieri to discuss Leicester's chances of winning an historic first top-flight title, the Foxes boss is now willing to contemplate a top four finish and a place in Europe's elite club competition.
They could seal a Champions League berth at Sunderland on Sunday and Ranieri highlighted the consistency in performances and results that his previously unheralded players have produced this term.
"Of course the Champions League would be fantastic," Ranieri said. "Can you imagine if next season Bayern Munich, Barcelona, Real Madrid and so on came here?
"That would be unbelievable for our fans and for everybody. It's a good experience. But now, it's about Sunderland."
A top-four place will be confirmed this weekend if Ranieri's side win at the Stadium of Light, Manchester United lose to Tottenham later on Sunday and West Ham drop points against Arsenal on Saturday.
"I think now we have opened the heart to everybody, the little normal teams and the normal players," Ranieri said.
"How many of our players were playing in non-league or small leagues a few years ago?
Jeff Schlupp returns to the Leicester squad after injury but, maintaining the theme of consistency, Ranieri is expected to keep faith with the regular starting line-up that has recorded five 1-0 wins in six games.
"Yes, it would be a surprise because they have (Riyad) Mahrez and (Jamie) Vardy, two of the top scorers in the Premier League, and they have clean sheets running right through the team," he said.
"They are a hugely well drilled, well organised, highly confident side to play against, to break down and to beat. You have to keep two of the best goalscorers in the league quiet
"They have has grown in confidence as the season has gone on. And, just as I think we have managed the pressure really well in the position we are in, they have managed the pressure magnificently up to now
Allardyce has also been impressed by Leicester's ability to adapt to their new status as title contenders in recent weeks.
"Earlier, on in the season maybe teams did not show them respect, but they gained everyone's respect when their form continued on into December," he said.
"You can see the change of tactics that they have used. They were an extremely good counter attacking side who they could break away and score two or three goals.
