"We've got an open mind about who the coach might be. I think there are one or two front runners, but I'm not going to mention them by name," explained Irvine, who said no appointment would be made before the 2011 World Cup.
"It is not rocket science to see who they would be. But a big problem will be the availability of coaches because this is a very serious commitment.
"In the past it has been the most successful and the best of the Home Nations coaches who have been candidates. But these chaps aren't always available because they have highly paid positions and their No 1 priority is to bring success to their national side."
Irvine, who toured with the Lions in 1974, 1977 and 1980 and was chairman for the most recent adventure in South Africa, suggested that his preference would be for the Lions to have a coach in place prior to the 2013 Six Nations and for that coach not to be tied to a national side that year.
Newly appointed Lions team manager Andy Irvine announced his arrival in his new post yesterday (Monday) by declaring he wanted his Head Coach to be in place at least 12 months before the tour and not to be coaching a national side in the 2013 RBS 6 Nations.
"I don't think it is feasible for the head coach to run the national side in the 6 Nations tournament prior to the tour," added Irvine.
"It would be asking too much of him and I think the national sides would baulk at the idea anyway because their national coach would have their eyes taken off the ball.
"I'm not ruling it out entirely, but I think it is unlikely he could do the two jobs."
Lions head coaches in the professional era
1997 Sir Ian McGeechan
2001 Graham Henry
2005 Sir Clive Woodward
2009 Sir Ian McGeechan