Following an injury to Mark Travers, there was a need to add a third goalkeeper to the squad to join Darren Randolph and Sean McDermott for the training camp in Portugal that will run until Tuesday, May 28.
Bristol City stopper O'Leary, 22, who qualifies for Ireland through his Kerry-born grandfather, has joined up with the squad and underwent his first training session on Saturday afternoon.
O'Leary is currently going through the process of becoming eligible for competitive games, so he will not be available for the EURO 2020 qualifiers against Denmark and Gibraltar.
"Max is in the process of getting his passport, so that is taking its time. But this is a good opportunity to have a look at him and for him to meet up with the lads," said McCarthy.
"He's had a very good season with Bristol City and was very keen to do what he needed to become eligible for us, so we will take a close look at him in training and leave the process of getting its passport up to our International Department.
"Max will give us another option at goalkeeper and he gets the chance to train alongside Darren [Randolph] and Sean [McDermott], and work with our goalkeeping coach Alan Kelly, for a few days in a great complex in Portugal."
McCarthy has also handed a first senior call-up to Bohemians keeper Talbot, who has been outstanding so far in his debut season in the SSE Airtricity League.
Talbot will check into Ireland camp on Tuesday, May 28 when the squad returns to Dublin and will be part of the match-day squads for the games against Denmark (June 7) and Gibraltar (June 10).
However, the 22-year-old will be released for his club games against Finn Harps (Friday, May 31) and UCD (Saturday, June 8) before linking back in with the Ireland set-up.
"We've had a couple of injuries to goalkeepers and Caoimhin Kelleher is going to the Toulon Tournament with the Under-21s, so we've brought in James Talbot due to his recent form with Bohemians," said McCarthy.
"Our goalkeeping coach, Alan Kelly, had been keeping an eye on the lad and he has done very well. We are happy to release him to play for his club. I've spoken to Keith Long and he's been very supportive. And he's delighted for James.
"We understand it's an important time for Bohemians but equally this is a great opportunity for James to come in with us."