Rodwell: Toffees can break into Big Four
"The top four sides are great sides but we are doing better and getting better," the 18-year-old midfielder told reporters.
"Hopefully we can build on the squad and next season push even more to get into the big four," said Rodwell, who has been touted as a future England international after his mature performances in the heart of Everton's midfield this season.
Manager David Moyes, whose side finished fifth in the league, has been massively impressed by Rodwell's contribution despite his tender years.
This season has already been "a dream come true" for Rodwell, who could start against Chelsea, one of the big four along with Manchester United, Liverpool and Arsenal.
"The FA Cup final obviously doesn't come about that much and Chelsea are one of the greatest sides in Europe," he said.
"But it is a 90-minute game and if we play well on the day then anything can happen so we will just take it like that, do well in the game and see what happens."