The Toffees currently sit seventh in the Premier League table, three points behind United and level with Arsenal but having played two games more than both of their closest rivals.
If Everton are to make up the difference between now and the end of the campaign then they will need to improve their form away from home, where they have won just two of their last 14 league outings.
That is in stark contrast to an eight-match winning streak at home, but Koeman insists that there is no difference in their approach to matches whether they are at Goodison Park or not.
"My meeting with the players is no different from when we play away to when we play at home. When the players play in front of their own fans they find themselves a little bit more comfortable but we go to West Ham and they still need points for this season," he told reporters.
"We can show we have a strong team and can play away from home in the same way we like to play at home and we will take up the challenge of trying to win all of our remaining games.
"Of course a top-five finish is still an incentive. It is our target; we know it's really difficult and a battle between Everton, Arsenal and Manchester United. The last game of the season is Arsenal vs. Everton and if we are still in the hunt, then to beat them will be really nice."
The Toffees take on West Ham United at the London Stadium on Saturday.