O'Neill's former club Leicester are top of the Premier League table and boast a five point lead over second-placed Tottenham Hotspur with only seven games to go. Claudio Ranieri’s side are in a position to complete a fairytale season that would see the club go from relegation survivors last season to Premier League champions this term.
The Ireland boss, who was in charge of the Foxes for four seasons between 1995 and 2000, claimed that his former club are a textbook example of what smaller teams can achieve against much bigger, and much more fancied opposition.
"I think they are the standard bearers for the smaller side, as it were, and I just think that they’ve given people hope now that you can compete," O’Neill said ahead of his side's Euro 2016 warm-up friendlies against Switzerland and Slovakia.
"In order to compete, you have to actually be successful but does that mean that just because they go on and win the league, does a smaller nation go on and win the European Championship? I’m not terribly sure about that."
Greece were the last side to win the European Championship as heavy underdogs, as they lifted the 2004 trophy after beating hosts Portugal 1-0 in the final.
While O’Neill will hope to emulate the fortunes of Greece and Leicester in France this summer, the Ireland manager remains very much grounded at this stage and acknowledges that his side hav been drawn in a difficult group.
"When the draw was made we had an opportunity at one stage, or we were in line to be drawn with lesser lights," said O’Neill. "But as I said before, I think with Italy, with what they’ve done in world football, I’m not so sure as if they feel as if they're a Pot Two team as it were, so effectively you’re looking at Italy and Belgium as Pot One teams.
"With that said, we’ve had our moments and it’s over now so we’ll just get ready for it. I think after [beating[ Germany the players feel as if they’re capable of dealing with that.
"Do we want to go in as underdogs? I think we will naturally anyway but I don’t think it’ll bother us."
Just as O’Neill acknowledged that Ireland will head into the tournament as natural underdogs, he also recognised that Ireland’s Group E opponents will be wary of the Boys In Green.
"I don’t think they will [underestimate Ireland]," said the former Celtic boss. "I think as Leicester are proving this year: you underestimate teams at your peril."
Ireland will face Switzerland on Friday at the Aviva Stadium before playing Slovakia just four days later on Tuesday evening and O'Neill is looking to use the two friendlies as an opportunity to try out untested players.
The 64-year-old indicated that Blackburn Rovers defender Shane Duffy would start at least one of the two games, while at least one uncapped player will start against the Swiss.
O’Neill would not specify as to which uncapped player that would be, but it appears Brentford midfielder Alan Judge may be the player he was referring to.
Judge has scored 14 goals and added nine assists this season for the Bees and O’Neill has mentioned his name at several junctures during the week.
Meanwhile Ireland’s all-time record goalscorer Robbie Keane has been ruled out of Friday’s game with a knee injury while Stoke City forward Jon Walters will most likely return to the squad on Friday night, and will definitely play on Tuesday according to O’Neill.