The in-form Toffees know a victory against the Premier League's bottom side will put pressure on Arsenal, which drew against Manchester City.
Martinez's side was beaten 2-1 by Martin Jol's Fulham in the Capital One Cup third round in September, although the Merseysiders avenged that defeat by beating Rene Meulensteen's team 4-1 in the Premier League in December.
Everton needed goals from Seamus Coleman, Gareth Barry and Kevin Mirallas in the last 20 minutes to earn that victory after Dimitar Berbatov's penalty had equalised Leon Osman's early opener.
Now Felix Magath, who replaced Meulensteen in February, will try his luck against in-form Everton, which has climbed to fifth in the table after a run of four successive wins.
Everton is currently seven points adrift of fourth-placed Arsenal with two games in hand, and takes on the Gunners at Goodison Park next Sunday.
However, before then it will meet a Fulham side fighting for its life, with Magath's men at the foot of the Premier League table and with no chance of exiting the relegation zone this weekend as they are four points adrift of 17th-placed Crystal Palace.
And Martinez is wary of an upset and what it would do to Everton's Champions League dream.
"He [Magath] brings an incredible amount of experience and he has had real success. He is very clear in the way that he gets his teams set up and I do feel that since he has been at Fulham they have been unfortunate in a couple of games," the Spaniard told reporters on Friday. "He will have found out a lot about his new players and I do feel this Fulham side is completely different from the one that came to Goodison Park and that they can perform really strongly from now until the end of the season, especially at Craven Cottage."
Magath returned the compliments in his own news conference, while also downplaying the impact Fulham's 5-0 defeat at Manchester City last week would have.
Fulham has shipped 70 league goals this season - Cardiff City is next worst with 58 conceded - and will need to be at its best to keep striker Romelu Lukaku quiet.
Lukaku has scored three goals in his last four league matches for Everton, giving him 12 in 21 top-flight starts this season.
Everton will be boosted by the likely return of captain Phil Jagielka, who Martinez says is "fully fit" after recovering from a hamstring injury.
John Stones is also fit despite suffering a nasty cut above his left eye in the win at Newcastle, but Steven Pienaar, Darron Gibson and Arouna Kone (all knee), defender Bryan Oviedo (broken leg) and striker Lacina Troare (hamstring) remain on the sidelines.
Fulham striker Kostas Mitroglou (knee) will be absent, and Scott Parker and Damien Duff are also ruled out with knee problems.
Ashkan Dejagah is expected to return after suffering a muscle injury, while Fernando Amorebieta is suspended, but former Real Madrid midfielder Mahamadou Diarra may feature after signing a pay-as-you-play deal on Wednesday. Diarra was released by Fulham at the end of last season.