McCarthy returned from five months out with a shoulder injury last weekend and produced an impressive performance in the 0-0 draw with Liverpool.
He had caught the eye in the Premier League before his injury and that had prompted talk the 23-year-old could earn international recognition with England.
Top-flight football appears unlikely to be on the agenda at the Madejski Stadium next season, but Adkins feels McCarthy could still be selected by England coach Roy Hodgson.
"I was at a goalkeepers' conference at the weekend and I spoke on Sunday and Monday at St George's Park," said Adkins.
"Jack Butland actually spoke. He's got an England call-up and he plays for Birmingham in the Championship so, in answer to your question, it's obviously a case that proved it's possible.
"The important thing for Alex, and all goalkeepers, is they want to be playing football.
"From Alex's point of view, he has been out for four or five months with a shoulder injury. He's come back ever so well from that. It was his first start at the weekend and he had a really good game, and he needs to keep building on that."
Chelsea and Liverpool have been linked with bids for McCarthy, but Adkins is not worrying about the prospect of losing the highly-rated keeper.
The Reading boss added: "There's talk about where people are going in the summer, but we've got good goalkeepers at Reading Football Club and Alex is one of them.
"He wants to play regular football and that's important."