Both players arrived at the Welsh outfit last month, but Ayew's hamstring injury has kept him out of action, while loanee King was unable to play against his parent club Leicester City last weekend.
The Swans head into the fixture one place above the relegation zone due to goal difference, and under the new manager, the team are unbeaten in their last four fixtures.
As for Burnley, who reside nine points off the top six, Sean Dyche has made one change, and it comes in defence as Matthew Lowton replaces Phil Bardsley, who is currently suffering with a hamstring injury.
The Clarets are winless in their last nine top-flight fixtures, but managed to earn a 1-1 draw with Manchester City last weekend.
Swansea City: Fabianski; Naughton, Van der Hoorn, Fernandez, Mawson, Olsson; Dyer, Ki, Carroll, Clucas; J. Ayew
Subs: Nordfeldt, Bartley, King, Routledge, Narsingh, A. Ayew, Abraham
Burnley: Pope; Lowton, Long, Mee, Taylor; Gudmundsson, Cork, Hendrick, Lennon; Vokes, Barnes
Subs: Nkoudou, Westwood, Wells, Ward, Lindegaard, Arfield, O'Neill
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