Sturridge has scored 11 goals from 21 appearances in all competitions for Liverpool this season, but has not been a regular starter for Jurgen Klopp since returning to fitness.
The 26-year-old's place in Roy Hodgson's England squad is believed to be in doubt, with the emergence of Harry Kane and Jamie Vardy pushing him down the pecking order.
But Sturridge claims "the cream rises to the top" and he thinks he still has the ability to make the difference for England in France.
"It's Roy's decision. Roy picks the team and I disagree that I shouldn't start," Sturridge told the Mail on Sunday.
"Why shouldn't I start for England? I disagree totally. I can start for England at the Euros. I'm not saying I should, I'm saying I can.
"Each game, they will select which players they feel are best on the day and I feel I can bring a lot to the table. I'd be the best player on the day because I believe in myself and my abilities.
"So I don't have any doubts about starting for England or who else plays for England. It doesn't matter. Names or any players don't mean anything to me at all."
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Sturridge, whose Liverpool side face Swansea City in the Premier League on Sunday, added he has "total faith" in himself.
"In life they say cream rises to the top. That's the one thing that my dad always used to say," the striker said.
"I have total faith in my abilities, total faith in what I can do on the pitch and I just have to focus on that, on my game and help the team be successful and I have no worries.
"I'm so relaxed in my life right now. So relaxed with everything that's going on and I don't look at anything that's going on anywhere else, but what's going on for myself and my team."