Chelsea, who are fifth in the league with eight games remaining, are also battling to finish in the top four to secure Champions League soccer next season.
"We have to try to do both," Conte told a news conference on Friday. "Every trophy is important for us.
"We fight until the end of every competition. Now there is the FA Cup. This is a quarter-final and if we win we play at Wembley."
Chelsea goalkeeper Thibaut Courtois has been questioned by some fans and pundits for his role in both of Lionel Messi's goals as Barcelona secured a 3-0 victory in their tussle at the Nou Camp to win 4-1 on aggregate and earn a quarter-final against Roma.
Conte says he has yet to decide if the Belgian keeper will keep his place in the starting line-up on Sunday.
"We are talking about two good goalkeepers - Thibaut (Courtois) and Willy (Caballero). Tomorrow I will pick the best player because we want to go to the next round," Conte added.
Chelsea have not lost to Leicester since December 2015, but the Italian boss is wary of the threat posed by the hosts' prolific striker Jamie Vardy, who has scored five goals in his past seven league matches.
"We have special plans to try to defend well," Conte said. "We know about Vardy and his characteristics."
(Reporting by Aditi Prakash in Bengaluru; Editing by David Goodman)
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