Stuart Lancaster's side are due to face New Zealand, South Africa, Samoa and Australia in the QBE Series, with the squad set to be named on October 22.
"Putting back the squad announcement has been great, it's really opened up the competition for everyone," Haskell told reporters.
"It means players are picked on form. The England shirt is never yours and it's a level playing field. I'm good friends with Chris. I've known him for years and I have the utmost respect for him, he's been a fantastic captain and is a great player.
"But I want his shirt, it's as simple as that."
Haskell, 29, has 51 England caps to his name and has played in all three back-row positions during a club career which has included spells in France, Japan and New Zealand.