Martin O'Neill has refused to answer questions about his future as Celtic manager beyond this season.
Martin O'Neill has been with Celtic for five seasons
BBC Scotland understands O'Neill wants time away from football to attend to his wife's poor health, with reports linking Gordon Strachan with the post.
"I've absolutely nothing to say about it. There's absolutely no word whatsoever coming from me," he said.
Celtic missed out on the title after a late collapse against Motherwell on the last day of the season.
O'Neill, who has been at Celtic Park for five seasons, made a point of applauding and waving to the travelling Celtic support after the final whistle, but said there was no special significance to the gesture.
"The support has been terrific," he said.
"I go to the crowd after every single game and I did today."
Former Aberdeen and Manchester United star Strachan quit Southampton in February 2004.
Strachan, 48, lost out to Walter Smith for the Scotland post late last year and has been working as a television pundit for BBC Sport.
But Strachan, who won 50 caps for Scotland, has made it clear he wants to return to management.
On Friday, O'Neill gave his strongest suggestion yet that he could be on his way.
"These five years have been pretty decent and there's as good a chance of me being here next season as not," O'Neill said after repeated questions about his future.
"But, if you are asking me if I'm going to join another football club, the answer would be no."
Last summer, Celtic made it clear they would allow O'Neill time off to look after his wife, who has suffered from poor health.
O'Neill, who spends much of the time at his family home near Wycombe, missed much of last summer's tour to North America as a result of his wife's illness.
He also pulled out of BBC television's Euro 2004 coverage for the same reason.