The Toffees are currently fifth in the table with 27 points from 14 matches, level on points with fourth-placed Liverpool.
"We do start to believe it's possible to finish in the top four now," The Mirror quotes him as saying.
"Honestly, we've always thought it is possible. I don't think we've ever started a season since I've been here where we have thought it's okay to finish, fifth, sixth or seventh.
"But now, I think, mathematically, we are starting to believe it's more possible. Look at our fixtures though - we need to get through December and January to really start to think about it."
Everton will take on Arsenal at the Emirates Stadium on Sunday.