Kilmarnock have won 16 over their 34 Premiership fixtures this season, which has led Clarke to be linked with both the Fulham and Scotland jobs.
Killie lost 1-0 to Aberdeen last time out to end a six-match unbeaten run, but Lennon is taking nothing for granted.
He added: ”In the first half of the season they were outstanding and they’ve had some good results against us recently. We’ll be expecting another tough game.
“I’m just looking for consistency and standards from here on in to be maintained to the cup final.”
Lennon's side are within touching distance of the title (Image: GETTY)
Lennon has impressed since taking over from Brendan Rodgers in January (Image: GETTY)
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Celtic could wrap up the league title this weekend if they win and Rangers fail to beat Aberdeen tomorrow.
The Hoops will also have one eye on the Scottish Cup final against Hearts in May as they look to complete another domestic treble.
“I know the players are more than capable of that,” Lennon stated about consistency.
“We’re unbeaten since January and have conceded three goals, yet there’s this wave of criticism which I think is well over the top.”
Celtic will play Aberdeen in the Scottish Cup final in May (Image: GETTY)