Though the Bhoys have three games in hand, they sit 21 points behind table-toppers Rangers and are set to lose the Scottish Premiership title.
With Celtic struggling to close the gap on the Gers, manager Lennon has come in for severe criticism and many have called for him to be sacked.
Former Bournemouth boss Howe has been mooted as a potential candidate to replace Lennon, but ex-Parkhead striker McInally cannot see the Hoops approaching him.
Recalling Celtic great Gordon Strachan’s words, McInally explained that the Bhoys managerial role is a job that most cannot turn down, but feels Howe will not be considered to take charge at the club.
“No, I don’t think Celtic will go for Eddie Howe“, McInally told Footy Accumulators.
“Would Eddie Howe take the Celtic job? I remember Gordon Strachan telling me ‘When Celtic ask you to be the manager of the football club, then it is not a job you can say no to, you say yes’.
“I wonder whether he would actually be asked to take the job in the first place.
“That will be an interesting one.“
Lennon is increasingly being tipped to stay at Celtic until the end of the season and will hope to apply some sort of pressure on Rangers over the coming weeks.