"Kone had a thigh problem but he's OK for Wednesday. Billy Jones is the only absentee," manager Sam Allardyce told reporters on Monday.
Saturday's come-from-behind win over Guus Hiddink's men left Sunderland on the verge of securing their top-flight status as they sit a point ahead of the bottom three and have a game in hand over relegation rivals Newcastle United.
Allardyce, however, warned his team against complacency and said he expects an Everton backlash, following Saturday's 3-1 drubbing by champions Leicester City.
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"There will be an instinctive response from Everton, so it's by no means a foregone conclusion," said Allardyce, who has never been relegated from the Premier League as a manager.
"We've still got to be very professional on Wednesday night. It's in our hands... We must take full advantage of our position and finish it on Wednesday. Don't come to the stadium with the expectation that it's job done because it isn't."
Sunderland finish their league campaign with a trip to Watford on Sunday.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
