Hull's Brady hoping to win race against time
Brady started the season in excellent fashion, scoring four goals from his first nine appearances.
A series of groin problems have hampered his campaign though, and after undergoing surgery last month, his season looked to be over.
But a quick recovery has the Republic of Ireland international hopeful of featuring at Wembley on May 17.
Brady told the club's official website: "I thought I'd be out for the season.
"But I'm a couple of weeks ahead of my rehab now and we have the FA Cup final against Arsenal at the end of the season so, hopefully, I'll be back in contention for that game.
"If I can get fit for the Everton game on May 11, that'll have me in good stead.
"There are international games coming up as well, which could give me a bit of game time under my belt."
Brady acknowledged that he may have rushed back on his last return from injury but says a repeat will not be happening, despite the frustration sitting on the sidelines gives him.
"Maybe I came back a bit soon (last time) but that was just me being eager," he added.
"I don't think there was anyone going to stop me coming back. If I felt I could play, I was going to play, but I have to be a bit more careful this time because I don't want anything flaring up.
"(Being injured) is a nightmare. I hate sitting around every week watching them getting ready for a game or going out training on the pitch when I'm going straight into rehab in the gym.
"My first season in the Premier League was almost a write off, but hopefully I'll get the last couple of games in."