The 23-year-old McCarthy has earned plenty of plaudits over recent weeks and pulled off a number of impressive saves as the relegated Royals lost 2-0 to Manchester City on Tuesday night.
Sergio Aguero and Edin Dzeko scored in either half to seal a comfortable win for the beaten FA Cup finalists, who were playing their first game since the sacking of Roberto Mancini on Monday.
With the Berkshire club set to play npower Championship football next season, players such as McCarthy could well find themselves in demand, but Adkins wants to keep his first-choice goalkeeper at the Madejski Stadium and will not be forced to sell him.
"I'm sure there will be lots of speculation," he said. "But we are in a good position in respect of the finances and there is good stability here.
"We're not looking to lose Alex and are looking to build for the future."