The 42-year-old, currently on international duty as assistant to Republic of Ireland and former Parkhead gaffer Martin O'Neill, stopped short of ruling himself out of contention for the post vacated by Lennon on Thursday.
However, questioned repeatedly on the topic after the Republic's training session in Malahide on Friday lunchtime, he repelled all advances.
Keane, who finished his playing career at Parkhead after leaving Manchester United and was tipped for the post by SportTimes legend Davie Hay, said: "I've got a job - I've got two jobs - I can't have another one.
"They are a brilliant club, an absolutely fantastic football club, one of the best in the world. But I have got a job."
He added with a smile: "I'm not taking a pay cut for anybody."
Keane's other job is his role as a television pundit, which will take him away from the Ireland camp for tomorrow night's Champions League final in Lisbon.
However, asked further what his response might have been if he was not employed by both the Football Association of Ireland and ITV, he replied: "I don't know, I haven't got a clue.
"There's always speculation when you are out of work or whatever.
"People might see this role as part-time or whatever, but it keeps me busy, I enjoy it.
"I'm happy with what I'm doing and if somebody calls me, I will speak to Martin and the FAI and we will have a look at it.
"But it's all speculation, and obviously that speculation comes from yourselves [the media].
"I don't think you have heard it from any club sources.
"As I said, I have got a job, we have got a game at the weekend, a busy old weekend coming up and I am looking forward to that."
The Republic face Turkey in a friendly at the Aviva Stadium tomorrow before meeting Italy at Craven Cottage and Costa Rica and Portugal in the United States early next month.
Keane was being quoted as a 16/1 shot for the job by William Hill yesterday afternoon after early favourite Henrik Larsson eased to 3-1 alongside departed United manager David Moyes with Owen Coyle heading the field at 9/4.