Warren Gatland will announce his squad to face Australia on Tuesday and is also expected to name his captain.
Some bookmakers have suspended betting on the captaincy, with Warburton the red-hot favourite and Irish duo, Brian O'Driscoll and Paul O'Connell, the skippers on the last two tours, in the running.
O'Connell was McGeechan's choice in 2009 but he expects the Wales flanker to wear the captain's armband Down Under.
"It's going to be an interesting one," said McGeechan in his role as ambassador for FirstCape wines in association with the Lions.
"I think Warren will be looking at Sam Warburton because he's worked with him.
"He knows him well, he's had him as his captain in the World Cup with Wales and you do have to have that captain-coach relationship."
While McGeechan believes Warburton will be handed the honour he also sung the praises of O'Connell.
"Paul was outstanding against Quins and he's the sort of player who brings out that passion and edge in the toughest of environments.
"It was almost his will that drove Munster to a win against a team that nobody probably expected them to beat.
"The plus is that he's hardly played any rugby this year so he's going to be fresh and, if he's 100% fit, then he's a good person to have on the tour because he understands the Lions and what they're about.
"He was a great captain in 2009 and, whether he's captain or not, I'd have him on the tour because you need people like that in the group, keeping the right focus at the right time and saying the right things at the right time."
Gatland is expected to name 37 players in his tour party and McGeechan, who has played a part in seven previous tours, reckons the could be afew surprises.
"He will be looking at the experienced players who've been around and wondering if there is still another tour left in them, and then looking at young players who might be able to step up when they pull on a Lions jersey," added McGeechan.
"Selection is a very interesting exercise. I think there will be some interesting mixes.
"Warren has never been afraid of making some interesting calls and I'm sure there will be some next week."