The 39-year-old missed Villa's 1-0 Premier League defeat to Burnley with a groin injury.
Given, 39, has started each round of the competition thus far, as well as three league games in recent weeks after his performances helped him reclaim Villa’s number one job from Brad Guzan earlier this month.
However, the veteran Irishman injured his groin in training ahead of the Premier League final-day clash with Burnley and is now in a race against time to make the Wembley showpiece against Arsenal.
Sherwood elected to give third-choice Jed Steer the nod for the 1-0 defeat to the Clarets, in what was the ex-Norwich stopper’s first league appearance for the club, but has stated that Guzan will be between the sticks next weekend if Given misses out.
Speaking after the match, the Villa boss said: "Brad will play [in the final if Given misses out].
"I have no idea what his chances are right now. We are assessing him each day. We are not ruling him out yet.
"If Shay wasn't to make it and Brad was to get injured we would have a problem.
"You wouldn't want to throw Jed in. He's not got a lot of experience in cup finals. The injury to Shay gave us an opportunity to look at Jed."
Kieran Richardson also missed his second straight game with a calf problem, as Charles N’Zogbia deputised at left-back, while Sherwood opted to rest centre-back Jores Okore due to the knee complaint the Dane has been dealing with in recent weeks.