Szczesny has started each of his club's 34 Premier League games to date this season, but has been rested for Arsenal's domestic cup matches, with fellow Pole Lukasz Fabianski taking over between the posts.
The latter has performed well in Szczesny's absence and saved two Wigan Athletic penalties as Arsenal secured a shootout victory at Wembley last weekend to book a place in the FA Cup final.
However, it remains to be seen whether Fabianski, who is out of contract at the end of the season, will be denied the opportunity to feature against Hull on May 17, with his rival keen to play his part in ending a nine-year trophy drought.
"I would love to play but it's the manager's decision. It's up to him," Szczesny told reporters.
"I think Lukasz has done really well and he deserves a lot of credit. I'm an Arsenal fan and I just want us to get the trophy.
"For us, it's important to get a trophy and hopefully we can appease everyone at the club."
After helping Arsenal overcome Wigan, Fabianski said he would "definitely be disappointed" if he was overlooked for the final.
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