Current boss Warren Gatland names his squad for the tournament on Tuesday, with Warburton widely considered as the favourite for the captaincy role.
"In 2009, we had our last selection meeting the day before the announcement. Then we slept on it and on the morning before the actual announcement we sat down again just to make sure we were all happy with our choices," McGeechan told Sky Sports News.
"The captain has to have the respect of his peers and has to be at the forefront of the squad but in the end it is often a personal choice; who the coach wants to be talking to on a daily basis who he has a good relationship with.
"The only caveat regarding Warburton is that there were rumours that he didn't want the Welsh captaincy position and the Lions position is obviously a much greater responsibility. As a player you want to be part of that tradition and part of what it is all about. When you are playing it is the biggest jersey you can wear."
The tour gets underway on June 1.