Alan Pardew and Craig Levein have been linked with the post and this week Ronald Koeman was quoted as saying he was considering taking over at Celtic although the Parkhead board, who have said all along that no decision will be made until the end of the season, strenuously denied that the Dutchman had been offered the position.
Lennon did his chances no harm as he extended his winning run in the SPL League to seven games with a 2-1 win over champions Rangers on Tuesday night.
Goals by Lee Naylor and Marc-Antoine Fortune were enough to secure the three points against Rangers who scored through Kenny Miller and finished the game with 10 men after Lee McCulloch had been sent off in the dying seconds after picking up his second yellow card.
A feisty Lennon told Walter Smith he should mind his own business after the Rangers boss had questioned the professionalism of the Celtic players during Tony Mowbray's failed reign which came to an end in March, then said: "I haven't been happy with the speculation.
"I understand you have a job to do but it is difficult enough to prepare for an Old Firm game.
"You have all the names thrown in and I'm led to believe it is total nonsense really.
"Don't ask me if a decision has been made. I will reiterate, they (the board) have made it clear to me that nothing will be done until the end of the season.
"But it was immensely satisfying."
Fortune, who had a goal chalked off in the last Old Firm game at Parkhead for his challenge on Rangers keeper Allan McGregor, had no fears about suffering the same fate when he headed past Neil Alexander, who had replaced the injured McGregor with only a few minutes played.
The former Nancy striker said: "The referee could not say it wasn't a good goal this time because I didn't touch the goalkeeper.
"I didn't look at the referee or linesman, I knew it was a goal.
"I was working hard and I really wanted to score in the Old Firm game so I'm happy.
"It was great result. We had to win and we did."
Fortune claims the Hoops' players would be happy to continue on next season under Lennon.
He said: "Lenny has done well, we haven't lost in the league under him.
"The chief executive of Celtic will decide whether he stays or not but there is a good feeling under Lenny.
"He is enthusiastic and tries to give us the energy that he has in him."