The Sunday Mirror says Kirkland was angered by the fact Leeds boss Warnock accused him of "going down like a ton of bricks".
It was after being confronted by Kirkland that Warnock issued an apology for the ridiculous comment.
The FA are investigating the incident in which Kirkland needed treatment after being pushed in the face by Leeds fan Aaron Cawley, following Michael Tonge's 77th-minute equaliser in Friday's 1-1 draw at Hillsborough.
Warnock yesterday apologised, saying: "I was out of order. Nobody should be allowed to come on the pitch and do that to Chris. After seeing it again I can understand why he was mad."