The veteran keeper is struggling to be fit for 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.
Sherwood said: "Shay's a doubt
We're assessing him every day, I wouldn't have played him today anyway
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."
Burnley made an instant return to the Sky Bet Championship after finishing second bottom and 11-goal Ings is expected to leave with his contract expiring in the summer.
Boss Sean Dyche has not ruled out the striker staying but knows he wants to play in the Barclays Premier League
He said: "Who knows (if he'll stay), probably not, just by the nature of his situation
Possibly? Who knows?
"I just think he wants a fresh challenge and a bigger challenge, He certainly wants to be in the Premier League - so does everyone.
"He has nicked a good goal and I thought he could have had another
He has played a big part over the last couple of years
He gets a lot of the headlines and I understand why but I wouldn't single him out against the rest of the group."
And Dyche wants to lead Burnley back to the top flight at the first attempt.
He said: "People keep coming up to me saying 'you're leaving, you're leaving' I don't know where that's come from
I've never said it once
I'm quite happy here
I believe in what the club has built.
"The Championship is a group of teams eager for the chance (of promotion), we have come out of it once
There are no guarantees but we have to work very, very hard."
Source : PA
Source: PA