With the Gunners not playing until Monday, the visiting side can move two points clear of its rivals for the final Champions League qualification spot with a win at St Mary's.
Having bounced back from a 3-2 home defeat to Crystal Palace with a 2-0 Premier League win against Manchester United last weekend - a result that prompted the departure of former Goodison Park boss David Moyes - Everton remains a point adrift of fourth-placed Arsenal, which undoubtedly has the easier run-in.
Arsene Wenger's men are due to host Newcastle United on Monday and West Brom before ending the season at Norwich City, while Everton meets Manchester City and Hull City after Saturday's trip to Southampton.
One factor that could work in Everton's favor at St Mary's Stadium is that Southampton has little to play for as the club closes in on a top-half finish.
That lack of incentive could go some way to explaining Southampton's recent run of having won just one of its last five games in the league, but the team's home record against Everton will be cause for optimism.
The Merseysiders have failed to win in their last four visits to the south coast and have triumphed in just one of their last 12 matches against this weekend's host.
If Everton can break that duck at Southampton's current ground, the club will win its fourth away league game in a row for the first time since December 1985, but Martinez knows it will not be a straightforward task.
"[In terms of] football concepts they're one of most attractive teams in the league," he told reporters. "There's a bravery about the way they play. Young players have big roles.
"It shows you the incredible progress they've had. We know we're going to face a really difficult team but in our eyes it's another very important game to be as good as we can. It's going to be one of the biggest tests we'll face this season."
Jay Rodriguez's season is over for Southampton and Mauricio Pochettino's men have not found the net in two games since the striker picked up a knee ligament injury against Manchester City three weeks ago.
Everton, meanwhile, will be without Kevin Mirallas (groin) for the remainder of 2013-14 and Lacina Traore (hamstring) is another set to miss the club's remaining three fixtures.
The visitors' biggest blow is that Sylvain Distin (hamstring) is unavailable for selection, and Martinez is reluctant to risk fellow center back Phil Jagielka (hamstring), meaning John Stones and Antolin Alcaraz will likely be partnered at the back.