The East Ayrshire club turned down a reported £350,000 offer for the 23-year-old Northern Ireland winger, who is under contract at Rugby Park until the summer of 2019.
Clarke said: “There’s been a bid, nowhere near acceptable. I would be a little bit sad if I was the player, to be honest, that the bid was so low.
“It was an easy one for the club to turn down.”
Rangers are also trying to sign Nottingham Forest striker Jason Cummings and Norwich City defender Russell Martin on loan.
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.