Under current boss Claudio Ranieri, Leicester have gone from being hotly tipped to be relegated to, at the very least, candidates to play in Europe next season.
It could be better than that, with Leicester showing no sign of letting up so far, having lost just once in the league to lead the way from Manchester City and Arsenal.
They won 3-2 at Everton on Saturday to open up a five-point lead at the top of the table, at least until City and Arsenal play against each other on Monday night.
O'Neill led Leicester from 1995 to 2000, winning the League Cup twice, but he never achieved the Premier League success the current team are enjoying
And when asked if Leicester could go on to win the league, O'Neill, now boss of the Republic of Ireland, told BBC Radio 5 Live: "It is an extraordinary run, it is absolutely phenomenal
"The very fact we're asking this question, it would seem ludicrous a couple of months ago even with the great, great start.
"Now you think this is actually possible.
"They've gone to Everton and got a fantastic result
They've only been beaten once this season, it's just incredible
And just for the very first time you're looking at whether the league is there for them or not
"You're starting to think there's gaps developing in European places and then Champions League, and you think it would have to be a fall from grace now not to make that.
"It's not true of course, but it's getting to that stage and it is remarkable."
Gerry Taggart, who played more than 100 games for Leicester between 1998 and 2004, agreed with O'Neill that Leicester are now genuine contenders.
"It is amazing, let's face it, to be top at Christmas," he told BBC Radio 5 live
"Leicester are defying all the odds now and this is not just a coincidence any more.
"Yesterday was another great result and another great performance and to go to Goodison and win against a good Everton team who are in good form themselves just proves this is no flash in the pan now, they've got to be taken seriously."
Northern Irishman Taggart admitted injury and suspension problems would hit the Foxes harder than most other challengers but added: " Robert Huth was out suspended yesterday and they brought in big (Marcin) Wasilewski
"People were saying he hadn't had the game time but he slotted in and did his job and they walked away with three points
"Especially in the front line (they need to avoid injuries)
There's a reason why (Jamie) Vardy and (Riyad) Mahrez are getting all the plaudits because they are top drawer at the minute
If one or both of them get injured then there could be trouble for them.
"But they just seem to just be going from strength to strength."
Source : PA
Source: PA