Jos Buttler was called into the squad on Tuesday morning as cover for Prior, who experienced some trouble with his thigh at the start of the week.
However, Cook is confident that Prior will be fit enough to keep wicket against the Indians at Trent Bridge tomorrow.
"Fingers crossed he should be alright. We're 99% certain that he'll be fine. We'll have a little check in the morning just to make sure," he told reporters.
Meanwhile, Cook has admitted that he is desperate to score runs during the five-Test series following doubts over his captaincy.