Worthington is keen to keep hold of the former Peterborough forward, who has become frustrated at the lack of first team action at Carrow Road, but the Sky Blues, who lost top scorer Gary McSheffrey to Birmingham last week, will have to up their bid.
"We got an offer from Coventry City for Leon on Tuesday or Wednesday last week and that has been ongoing," the Canaries boss told the club's website. "The club flatly refused the offer. I don't want to sell the player, but there is a price which he will be sold at."
McKenzie was left out of the weekend trip to Derby because it was felt his mind wasn't right. Worthington added that any money brought in for the striker would be put towards the sort of player he wants, thought to be a target man.