In the sides' 17 meetings to date across all competitions, the Welsh outfit have yet to taste success, with Everton winning 12 and drawing five.
Roberto Martinez will be confident of extending that impressive run given his side have lost just once in the top flight all season.
Everton have conceded only 15 goals, the joint-lowest total in the Premier League, and go into the game buoyed by a 4-1 win over Fulham at Goodison Park.
Martinez's men could go second in the table with victory over the club he previously captained.
The Spaniard also began his managerial career at the Liberty Stadium and has paid tribute to Swansea's achievements in recent years.
"(I will go back with) great emotions because I have a soft touch for Swansea (but) it is not about managers, it is an important game for both clubs," he said.
"(We are) two clubs with similar philosophies and it's going to be a real test for us.
"What Swansea have achieved in the last 10 years is incredible. They are a real model of how to develop a way of playing and be successful with it."
Martinez will be without Gerard Deulofeu (hamstring), while Leighton Baines (ankle) and Tony Hibbert (knee) are unlikely to recover in time for the trip.
Swansea have lost just twice at home in the top flight this season, reversals against Manchester United and Arsenal in August and September respectively.
Michael Laudrup's men sit 10th in the table, but cannot improve their position this weekend should they defy a lengthy injury list to beat Everton.
Nathan Dyer hurt his ankle in Sunday's 1-1 draw with Norwich City, while goalkeeper Michel Vorm has undergone knee surgery.
Michu (ankle) is another player suffering injury trouble, although both Leon Britton (foot) and Chico Flores, who was suspended last time out but has also been hampered by a knee problem, could return.
Assessing Martinez's work at Everton, Laudrup said: "In the last 10 years they are around the top half of the league, and that was with a smaller budget that a lot of teams. So to come in and want to change the way of playing is even more difficult.
"I have watched their last four or five games and they were outstanding against Arsenal (in a 1-1 draw) at the Emirates.
"They have kept a lot of their best players and made a huge signing in (Romelu) Lukaku on the final day of the transfer window."
