Roberto Martinez's side have games in hand on the teams around them, Manchester United and Tottenham Hotspur, and will go above fifth-placed Spurs with victory over the Swans.
Everton have only lost once at Goodison Park this season and with Swansea winless in four games and without league success on the road since November, there is room for the Merseysiders to be optimistic.
Loan striker Lacina Traore, who has yet to play a top-flight game since arriving from Monaco, is "ahead of schedule" in his recovery from a hamstring problem, but is not expected to be fit until late April.
Phil Jagielka could be back to captain the side in central defence after missing their last four matches. Both he and Gareth Barry, who has a slight calf strain, face late fitness tests ahead of this weekend.
England World Cup hopeful Ross Barkley will likely have to settle for a place on the bench, but another bright young talent, Gerard Deulofeu, should be maintained in the starting XI after scoring against Cardiff.
Their 22-goal top goalscorer from last season made a 30-minute cameo appearance in the 2-1 home defeat to West Bromwich Albion last Saturday, which leaves the Welsh outfit only four points above safety.
Possible starting lineups
Everton: Howard; Coleman, Jagielka, Distin, Baines; Barry, McCarthy; Deulofeu, Osman, Mirallas; Lukaku
Swansea: Vorm; Rangel, Amat, Williams, Davies; Canas, Britton, De Guzman; Lamah, Routledge; Bony
Sports Mole says: 2-0