Having already interviewed Kevin Blackwell yesterday, the Leeds chairman Gerald Krasner wants to find out if Moore has the credentials to take charge of the club in the First Division.
Moore is in his eighth year at Rotherham and has kept the club in the First Division for three seasons since winning back-to-back promotions from the Third Division from 1999 to 2001.
Attempts to entice Gordon Strachan back into management have been shelved and instead Moore has been identified along with Blackwell and Wigan's Paul Jewell.
Neil Warnock and Joe Royle are at the top of a back-up list along with Stan Ternent, lately sacked by Burnley and Peter Jackson of Huddersfield.