Deila’s position had come under increased scrutiny following Sunday’s William Hill Scottish Cup exit to Old Firm rivals Rangers, and the 40-year-old Norwegian’s summer exit was confirmed on Wednesday morning.
Lennon played for Celtic between 2000 and 2007, managed them between 2010 and 2014 - with Deila then replacing him - and has been out of work since his departure from Bolton in March.
On the possibility of succeeding Deila, the Northern Irishman told Press Association Sport on Wednesday: “I would definitely be interested.
“I am not promoting myself for it but you have asked an honest question and I am giving you an honest answer.
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“I think you always do (miss being part of Celtic). I was associated with the club for 15 years, I missed it when I left as a player and there are aspects that you miss even now at 44 years of age.
“You see events like Sunday, the passion and the crowd and what it means to so many people, there are not many clubs like it, that can generate that sort of enticement.”
As part of the statement on Celtic’s website on Wednesday morning about the news, Deila said: “It is vital that the club comes first, instead of me being the focus.
“Hopefully now the team and the club can be the focus as we enter this final important period of the season.’’
Celtic have an eight-point lead over Aberdeen with five games to go in the Ladbrokes Premiership, but some angry Hoops fans demanded Deila be sacked immediately after the penalty shoot-out loss to Mark Warburton’s men.
The Parkhead side’s hierarchy was understood to be concerned by the lack of progress under Deila during his two-year reign, with the former Stromsgodset boss also reportedly left weary by the constant speculation over his future.
Deila, who was on a one-year rolling contract, acknowledged he had encountered some “disappointments’’ during his tenure, but said he had always given his all.
“There have been some disappointments and times when we have not achieved what we had hoped for and I’m realistic and honest enough to admit that, but I know that the players, myself and my backroom team have always given everything we had to bring success to our supporters.’’
He continued: “It was an absolute privilege to be named manager of Celtic, such a wonderful football club, and I have enjoyed my time here immensely.
“I will never forget the welcome I received almost two years ago at Celtic Park from so many fans. When I joined Celtic I knew I was coming to one of the world’s great football clubs.’’
Deila led the Glasgow giants to a league and cup double last term and is aiming to deliver the club’s fifth successive Scottish Premiership title.
“My total focus now is on retaining our Premiership title and making it five in a row for our great club and proving that we are the best in the country,’’ he said.
“Myself and the players will be giving everything we can to achieve this and I know that starting on Sunday we must all unite and drive the club on and really go for what we all want as Celtic supporters - to be Scottish champions once again.’’