NI boss O'Neill: Leicester 'tempting' but I'm not looking for new job
The Foxes hierarchy will this week meet with caretaker boss Craig Shakespeare to discuss his prospects for the role and the case for Ranieri's former number two has been strengthened by back-to-back victories since the Italian was axed.
Others have been sounded out about the vacancy, though, and both former England boss Roy Hodgson and current Northern Ireland chief O'Neill have reportedly been on the club's wishlist.
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Hide AdO'Neill guided his country to the knock-out stages at Euro 2016 last summer, their first major tournament finals in three decades, and they are well placed to attain a play-off berth for World Cup qualification in 2018 having started their campaign well.
The 47-year-old has three years remaining on a deal that includes a £750,000 release clause but admits the lure of Leicester would intrigue him were they to come calling.
"I think you're always tempted - you have to consider these things if the opportunity is presented to you," O'Neill told BBC Sport at the unveiling of a new education and heritage centre at Belfast's Windsor Park.
"I have a good relationship with the board and the (Irish Football) Association here. I've been in the job five years now and I'm contracted for another three.
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Hide Ad"I don't think you can ever say 'no' in football. Equally I'm not actively looking for another job; I've said that all along.
"When vacancies have arisen, particularly in England this year, my name has been mentioned but I actively haven't sought to find another job outside the one I'm in.
"That won't change over the course of my contract and if an opportunity presents itself, the association and myself will sit down, look at it and see where we go from there."