The Toffees are having an impressive 2012-13, losing just twice in their 18 Barclays Premier League games so far and currently lie fifth in the table, behind fourth-placed Arsenal on goal difference alone.
Martinez is backing David Moyes' side to be challenging for a Champions League berth right up to the end of the campaign and expects a demanding assignment for the Latics on Merseyside, where Everton are unbeaten this term.
At the same time, though, the Spaniard is feeling optimistic ahead of the contest having seen his team only denied a home victory against Everton earlier this season when Leighton Baines' late penalty for the visitors ensured a 2-2 draw.
Asked if he thought the Toffees would be able to sustain their top-four push, Martinez said: "Yes, because of the experience they have got and because of the way they have started the season.
"We all know that Everton traditionally start seasons a little bit slowly and then finish at a very good level.
"But we can speak from our own experience. It will be our second game against Everton and in the first one, it was the best Everton side we have faced.
"This Everton side tick every box. They have been able to get consistently good results in this league and that allows you to be fighting for the top four positions.
"At Goodison Park they are unbeaten and it is one of the hardest places to visit in the Premier League.
"We are well aware of all that, but we feel we can match Everton on our day."