They are now back under Scottish Rugby Union control, having been franchised to brothers Bob and Alex Carruthers.
The change has raised fears Larkham will not make the move to Murrayfield, and the SRU have yet to make an announcement either way.
Fly-half Larkham, 33, is due to arrive after the World Cup but could become available if Edinburgh decide they cannot fulfil the commitment the previous management struck with the Brumbies player.
Leeds chief executive Gary Hetherington said: "We are just waiting to see what happens. We are having a meeting and we will discuss the situation."
Hetherington told The Australian newspaper: "We would have an interest in Stephen Larkham because we are looking to strengthen our team.
"He is a player who would be of interest to us. We are looking to add a world-class player to our squad and Stephen Larkham would fit that bill.
"Stephen is currently under contract to Edinburgh so we are not in a position to enter discussions with him."
Hetherington confirmed a move for Larkham would be possible within Leeds' current budget.