Without confirming a name, FSU said in a statement Saturday that the school will introduce its next coach at a news conference at noon ET on Sunday.
Norvell guided Memphis (12-1) to its third straight appearance in the American Athletic Conference championship game, with the Tigers prevailing over Cincinnati 29-24 on Saturday.
After the game, Norvell declined to answer ESPN's questions about the Florida State job.
The transformation of Memphis' program under Norvell has been stunning. The Tigers have won eight or more games for six straight seasons, and Norvell has been at the helm for the past four. From 1974 to 2013, the Tigers had just two seasons of eight or more wins.
One of the youngest head coaches in the country when he took over at Memphis, Norvell, 38, would replace Willie Taggart at Florida State. Taggart was fired nine games into his second season at FSU earlier this year. He was 9-12 in 21 games as FSU's coach.
Norvell is one of the most respected offensive minds in college football. Memphis has set multiple school records on offense and scored 30 or more points in 43 of the 53 games of his tenure.
He was the offensive coordinator at Arizona State under Todd Graham before getting the Memphis job and prior to that worked under Graham at Pittsburgh as the co-offensive coordinator and at Tulsa as the passing game coordinator.