The Blades frontman picked up the muscle injury after taking part in extra shooting practice after he missed a golden chance at home to Southampton recently.
He is nearing fitness again, though, and may travel at the last minute to Georgia or Switzerland as the Republic face a crucial couple of qualifiers as they look to seal their place at Euro 2020.
Shane Duffy, of Brighton, is in a similar position after picking up an injury while playing for his club, and McCarthy said: “I think they have a chance to play. I got a message from Shane earlier on, he’s feeling good.
“He didn’t say he was fully fit or ready to go, just that he’s feeling good. He’s optimistic. I haven’t spoken to Didsy (McGoldrick) for a while, for a couple of days. But Chris Wilder mentioned that they’re doing everything they can to get him fit. I’ll wait as long as I can.
“I just told Shane, I responded to his message, I said, ‘the plane’s leaving at 2 o’clock from Dublin airport to Tbilisi (on Thursday) so we’ll keep a seat with extra legroom for you, as we normally do, don’t be late.
“Didsy, he’s been on the grass, he’s been training. As I said, I’m far more optimistic about them being involved. But, you know, if they don’t come to Tbilisi, they can get a flight to Geneva and we’ll see them there if they’re fit for that game.”