Everton manager Ronald Koeman is targeting six points from their next two matches to retain some purpose in their season.
West Brom and Hull are the visitors to Goodison Park before the Toffees head to near-neighbours Liverpool for the Merseyside derby.
Koeman has challenged his players to win both games at home in order to maintain the pressure on teams in the top six, with fifth-placed Arsenal only six points away, albeit with a match in hand, but seemingly in crisis.
"I still believe in when we win the next two games at home that still something is possible above us in the table," said Koeman.
"But that starts with six points and starts this Saturday.
"Arsenal are normally strong and have good players, so it will be really tough to catch them. But maybe after six points then we come closer and then maybe something is possible.
"It starts always by yourself, don't look too much to other teams. If you win we come closer and that is the most important."
A victory over the Baggies, one place below in eighth, would open up a significant gap and virtually assure the Toffees of seventh place.
Koeman thinks that would represent a degree of success this season after back-to-back 11th-placed finishes under predecessor Roberto Martinez.
"The first objective is for Saturday, to win the game and make the distance to seven points. I think that is really a big gap," the Dutchman added.
"That (seventh) is the first step we needed to make for this season.
"I don't like to speak a lot about the end of the season but if we finished in seventh I think we can be happy.
"The next step needs to be for next season."
Everton's nine-match unbeaten Premier League run, stretching back to mid-December and garnering 21 points, was ended by a disappointing performance at Tottenham last weekend.
However, Koeman does not believe that will affect his players and instead said he thought it provided a timely reminder of where Everton currently are.
"We know Tottenham are a really strong team. They were the better team that day and it is good to see sometimes that still we need to improve," he said.
"I don't think it will affect the team a lot. It shows that still there is a lot of work to do."