The Kilmarnock boss was furious with the performance of the whistler, who sent off three Killie players in the home side’s 1-0 defeat to Aberdeen on Saturday afternoon.
He would later wonder whether McLean referees Kilmarnock matches evenly because his father Stuart McLean made over 450 appearances for the Rugby Park club.
Clarke could now find himself on the end of an SFA sanction for the comments, with a decision expected to be made tomorrow.
The Killie boss told the press: “I went over and congratulated him (McLean) and told him it was the worst performance I had ever seen in my career - and it is a long career.
“He lost control of the game in the first half. He actually lost control of a professional football match.
“I feel a little bit sorry for him. People tell me historically that he has never been particularly kind to Kilmarnock.
“I think he feels the pressure of the fact that his father played so many games here. I really do.
“I have mentioned it a couple of times privately but publicly I am saying now, I think it would be better for Steven and Kilmarnock if Steven doesn’t referee any more games for us. Quite simple.”