The rivals clash at Goodison Park on Sunday in a match that could be decisive in the race for the final Champions League qualifying spot.
Everton amassed a fifth successive Premier League victory with Sunday's 3-1 triumph at Fulham and they are now just four points adrift of Arsenal.
If they win all seven of their remaining games, Roberto Martinez's side will finish fourth.
The outcome of their last clash with Arsenal was a 4-1 FA Cup drubbing on March 8 and Howard has revealed a desire to avenge that result.
"We are looking forward to playing Arsenal," the American goalkeeper said.
"We still have a sour taste in our mouth about what happened at Emirates Stadium in the FA Cup, so we will try and put that right at home.
"Two weeks ago we were looking to catch Tottenham, now we are asking ourselves 'can we catch Arsenal?'.
"We're not favourites to finish fourth because gap is still four points.
"It's in our hands because we have a game in hand and we have to play them, but there is still have that four-point lead so it is difficult.
"We are on the outside looking in, but we are in the fight. If we could win next week and keep on their heels, that would be important for us."
While Everton are gazing upwards at the dizzying prospect of joining Europe's elite next season, Fulham are desperately plotting their Premier League survival.
Rooted to the foot of the table with six games left to secure a 14th campaign in the top flight, their chances of bridging the five-point gap to safety appear remote even if Hull, Norwich and Crystal Palace are due to visit Craven Cottage.
John Heitinga, who wore a Zorro-style protective mask against Everton having undergone surgery to repair a broken nose last Tuesday, refuses to throw in the towel.
"We have six games left and we have to believe. We have to keep giving everything," said Heitinga, who arrived at Craven Cottage on a free transfer from Everton in the January transfer window.
"We deserve credit for the way we played against Everton but it was not enough. We have to keep fighting.
"If the team can perform like we did against Everton, there are still 18 points to play for.
"I knew it was going to be tough when I joined, but when I see the quality in the squad and the performance against Everton, I know we have to keep fighting."