The Costa Rican international is looking for new coach Roberto Martinez to push the Toffees on and compete with the Premier League elite for a top-four finish.
"I hope to have a year with a lot of chances to play and to help my team to qualify for the Champions League," Oviedo told Marca TV.
"Obviously, it is what everyone at Everton and all the fans want. We all want Everton in the Champions League."
Oviedo joined Everton last summer from Copenhagen and has enjoyed his first year at Everton and in England.
"Compared to Denmark, England is another thing altogether. It is great for my family and I am at a club, an excellent club, where everyone wants to help and there is a real community feel," he continued.
"This is one of the biggest clubs in England and everything is in place. I could want nothing more."