Vice-chairman Aiyawatt Srivaddhanaprabha confirmed he would talk to the manager in the summer with a fresh deal on the agenda following his stunning success with the Foxes
Italian Football Federation president Carlo Tavecchio wants Ranieri to coach Italy to a World Cup win - with current boss Antonio Conte joining Chelsea after Euro 2016 - in the future after he clinched the title with the 5,000-1 shots this season
But Aiyawatt, known as Top, is ready to sit down with Ranieri after they finish the season at his former club Chelsea on Sunday and discuss his future at the King Power Stadium.
"At the end of the season we will talk about that with him," he said
"We will sit down together, it's not fair to talk now with one game to go. When we talk about something, it's long term, not just until September.
"I like people to work for me when they are happy and enjoy working with the group of people."
The Italian has always played down the need to sign a new deal after he penned a three-year contract as the surprise choice to replace Nigel Pearson last year.
He won the Enzo Bearzot award as Italy's coach of the season in Rome on Monday.
Ranieri admitted he was snubbed by Championship clubs following his dismissal from Greece in 2014 but Top, son of Leicester owner Vichai, insisted they never had any doubts about the 64-year-old
He said: "No, we believed in him. We felt he wanted to be a success. I know everyone wants to be a success but he was the right guy with the plans, the right guy who said what we wanted to hear. That is very important when we interview someone.
"I asked him (about Greece) because I wanted to know. He answered everything very clearly, why he failed there, why things happened in the past. I love his character and the way he talks. And now you have seen how he takes the pressure off everyone and the club. He knows how to manage that well."
Source: PA