Keane and McCarthy both missed Ireland's warm-up matches against the Netherlands and Belarus due to injuries but despite their fitness struggles, the pair was included in the final 23-man squad for Euro2016.
O'Neill has now gone on to deliver an update regarding the health of LA Galaxy striker Keane and Everton midfielder McCarthy and has revealed that he expects the two players to be fit in time to feature in France in just over a week's time.
The 64-year-old said: "He (Keane) thinks that he could be. If it's not (the group opener against) Sweden, he thinks he'll be fit for the second game (against Belgium). That's the thoughts at this minute. But I'm not a doctor.
"Robbie is the captain of the side, Robbie feels he is going to be fit.
"James McCarthy did a little bit of work today and there was a good improvement in that sense. That helps a lot.
"I'm not a soothsayer, but I think that there's a fairly decent chance that they are going to be okay. We have got a little bit of time.
"James came off in that last game, but he has played a lot of matches for Everton, obviously, he's a pretty fit lad anyway at the best of times, but like anything else, you'd like some time on the field.
"But we can organise games while we are out in France, we have a little bit of time if that's the case - and even before that because we have got a week's training to do here."
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