The veteran keeper is struggling to be fit for the clash at Wembley on Saturday after missing the 1-0 defeat to Burnley.
He had just returned to Villa’s league side after almost three years without a Barclays Premier League appearance.
Jed Steer made his top flight debut against the Clarets, with Brad Guzan on the bench, and was beaten by Danny Ings’ sixth minute winner.
“Shay’s a doubt. We’re assessing him every day, I wouldn’t have played him today anyway,” said Sherwood.
“You don’t often get the chance to look at a young goalie and you can only really assess them on the stage and I thought Jed did all right. We’re not ruling Shay out yet.”
But Sherwood confirmed Guzan would start against the Gunners next week if Given fails to recover in time from the injury he suffered in training.
“Yes,” he said. “You wouldn’t want to throw Jed in, he’s not had much experience in a cup final. With the injury to Shay it was an opportunity to look at Jed.
“If Shay wasn’t going to make it and Brad was to get injured we’d have a problem.”
Villa finished fourth bottom after another fight against relegation and Sherwood, who replaced Paul Lambert in February, knows he must change things next season after their final day defeat.
“It tells no lies, where you finish in the league is where you deserve to finish,” he said.
“We have a lot of players, and we can’t just keep bringing them in. The mentality needs to change, it’s been a club used to losing games and it’s not good.”