Celtic were heading for top spot when they went 2-0 ahead against Inverness in their most recent match on November 27, but the Highlanders stunned them with two late goals.
Neil Lennon's side also lost a lead in their previous encounter, when Sean Dillon's injury-time header earned Dundee United a point at Parkhead.
With Rangers' trip to face Dundee United at Tannadice being postponed, Celtic will go top on goal difference if they beat Killie, who have won five of their last seven games.
So South Korea midfielder Ki knows they must improve their focus, saying: "We always get the chance to go top but we always miss the chance.
"We have to be mentally stronger. This is our home game and we have to win for the fans as well."
Kilmarnock continued their impressive form with a 2-1 victory over Hibernian on Saturday, while Celtic endured a third consecutive weekend without a game.
"It's going to be an advantage for them because they have played," Ki said.
"It is a concern that we've not played for three or four weeks," he added.