Stewart Regan quit the role on Thursday after nearly eight years in post, leaving Scottish football’s governing body seeking a new chief executive as well as a new national team coach.
And support is growing at Hampden for the Hibs chief to replace the former Yorkshire County Cricket Club chief executive as a result of her work with Motherwell and the Easter Road club.
And Lennon, Dempster’s head coach at Hibs, spoke warmly of the former account director at an advertising agency, describing her as “very, very good at what she does”.
He said: “She can handle anything, trust me. If she can handle me, she can handle anything.
“If you look at whats she’s done at Motherwell, she did great things there, and the turnaround here since she came in.
“You’d have to ask Leeann the question, I don’t know what the SFA are looking for in the role they want from the chief executive, but it doesn’t surprise me that she’s being linked with it. We all hope here [at Hibs] that she doesn’t go.
“She is media savvy and behind the scenes she knows the Scottish game inside out, knows all the boards, all the directors and how they work.
“She doesn’t come to me and start talking tactics and formations, she leaves that to me, but in terms of how to run a football club, she has done an amazing job wherever she’s been.”
Lennon insisted that the act of replacing Regan should be a quick process, warning: “There’s a huge vacuum there now that needs to be filled.
“There’s a national manager to find and someone to actually get a hold of things and run the game accordingly on a more professional basis.”