The Irishman has not played for three months since undergoing groin surgery back in February.
He was not expected to be available for the Wembley showpiece, but boss Steve Bruce revealed Brady could be in the frame.
"Robbie Brady's come from nowhere in the last couple of weeks. It's amazing what an FA Cup final does," Bruce told the Hull Daily Mail.
"We've seen him in training for the first time in six months, so it's been incredible."
Brady, a former Manchester United youth team player, had scored four goals in 18 appearances for Hull before succumbing to injury.