Robbie Keane and James McCarthy are facing a race against time to be fit for the Republic of Ireland's Euro 2016 opener against Sweden.
Both men were included in the final 23-man squad named by manager Martin O'Neill shortly before Tuesday night's 11pm UEFA deadline despite playing no part in either of the final two warm-up games against Holland and Belarus.
Striker Keane is battling a calf problem picked up on Saturday, while midfielder McCarthy only resumed training on Monday after being hampered by the thigh injury with which he reported for duty.
O'Neill said: "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."
Midfielder Harry Arter, who damaged a thigh muscle in training ahead of the Belarus game, which ended in a 2-1 defeat at Turner's Cross, was not so fortunate with O'Neill unwilling to take a further gamble.
He said: "Harry has picked up an injury at this minute and has gone home. He is feeling that he could be fit in maybe 10 days or something like this. But it's another call then."
There was a place in the squad for 40-year-old Shay Given, who became Ireland's longest-serving international on a night when goals from Mikhail Hardzeichuk and Maksim Valadzko won it for Belarus despite Stephen Ward's late strike.
That meant disappointment for David Forde, who was among the men discarded.
O'Neill said: "He took it like I would expect David to take it, like a proper man that he is, but a natural disappointment - which I expect - and that's the way it was."