The former defender says they must build around their young stars to make the top four.
Roberto Martinez has a young and talented squad at his disposal this season, with Ross Barkley, John Stones, Gerard Deulofeu, Romelu Lukaku and Brendan Galloway all under 23 years old.
They have all impressed, although it is forward Lukaku who has enjoyed the best form with 14 goals in all competitions to his name, the latest against Palace being his 50th for the Blues.
He and his fellow youngsters form a talented spine at Goodison Park, and Stubbs says the club must build around them to try and challenge for the Champions League.
“If Everton are going to become a top four team they have to build a team around these young players,” he told TalkSport.
“You look at the Everton team and the players now, whenever they get the ball they look like they’ve got lots of options and are full of confidence”
“Lukaku is unplayable at times and Ross Barkley and Gerard Deulofeu; they all want to take the ball into tight areas. Everton look very exciting at the moment.”
Even though Everton are currently 9th in the table, the open nature of the league means they are still very much contenders if they can put together a run of results.
They are on 22 points at present, but just one point behind Crystal Palace in sixth and four points behind Tottenham Hotspur in fifth.
Manchester United and Manchester City are seven points away in 3rd, meaning results going in their favour could see them pushing for a place in the top four at some point.