The midfielder has impressed on loan at Crystal Palace this season, and his performances have earned him a key role in Gareth Southgate's side.
"It would be stupid to rule us out. I think we have a really good squad, and the squad is young and youthful," Loftus-Cheek said.
"But we are all here on merit on how well we performed this season. In training, you look at our talent and mentality, it is frightening. We have a good chance.
"I think we are special team because the squad is still young but so good at the same time. If we can deliver when it matters, and I think the boys can do that, then we can have a really good tournament.
"Looking into the future, as we are still so young, we can really develop into a top team."