The name Danny Ward has been mentioned, so has Danny McGuire, whilst Ryan Carr and James Webster have also been touted.
Whilst the Daily Telegraph Down Under believes the favourite is former Featherstone Rovers head coach Ryan Carr, the bookies are telling a different story.
Tony Smith is now the lead favourite at 5/2 with Danny Ward close behind at 7/2.
Ryan Carr is at 5/1 as is former Brisbane Broncos boss Anthony Seibold, with Shane Flanagan – the former Cronulla Sharks head coach who was rumoured with Leeds last year – at 6/1.
Even former Warrington Wolves hooker Michael Monaghan is priced at 8/1 and Penrith Panthers assistant coach Cameron Ciraldo at 10/1.
Meanwhile, Jamie Jones-Buchanan is at 12/1, but James Webster and Danny McGuire sit down the table at 16/1.
Rhinos chief executive Gary Hetherington said the hunt had started to replace Agar, but that it would not be rushed.
“We do plan to appoint a new head coach and will apply a comprehensive recruitment process but there is no predetermined timescale for this appointment,” Hetherington said.
Leeds take on Castleford Tigers in the Challenge Cup Sixth Round on Saturday with the winner progressing to the quarter-finals and one step closer to the Tottenham Hotspur Stadium.