The 23-year-old squad was named in Roy Hodgson's Three Lions squad for the friendlies against the Republic of Ireland and Brazil earlier this year but did not make an appearance.
And McCarthy caught the eye again with a man-of-the-match performance in Saturday's 1-1 draw against QPR.
"I keep highlighting to Alex that he is an exceptional goalkeeper," Adkins told the Royals' official website.
"He comes and catches crosses better than anyone and his shot stopping is magnificent.
"Is he far away from England? No, not at all. I know they'll monitor all the 'keepers and I spoke to Roy after he went to Brazil with the squad in the summer.
"That was important, all he can do is keep playing on the pitch."