Head Coach McGeechan has his sights set on taking "35 players fit and ready to play" to tackle the Springboks, and has already pencilled in two-thirds of his squad.
In an interview with the Daily Telegraph, McGeechan stressed that he and his fellow selectors will have "an open mind" on the final few places right up to the time of announcing his tour party on April 21.
"This is the biggest challenge the Lions have ever faced. The Springboks are settled and are used to winning, they've got a consistent group of senior players, their back-up strength is impressive and their provinces are strong. Factor in, too, that we've got fewer lead-in games than ever before and it's a formidable prospect," McGeechan told the Telegraph's Mick Cleary.
"We need to leave for South Africa with 35 players fit and ready to play. If someone selected then picks up, say a four-week injury just before we depart, they'll have to go on standby.
"There are still places up for grabs. The final 10 names are invariably what selection is about - we've got to make sure we get the chemistry just right.
"We've got to have an open mind right up to a few days before the Test. We can't jump to conclusions early. Everyone will have a crack at that Lions spot."
McGeechan also claimed he is still pondering over who will captain the tour party. "The captain has got to have a strong character, the respect of others and be able to pull things together quickly. He's got to give off the right tone, be able to deal with tricky situations. There are still three or four names there."
Any remaining ill-feeling between the Welsh and Irish following Warren Gatland's claim that his players disliked the Irish teams in the build-up to the Six Nations decider has been dismissed by McGeechan. Gatland, along with fellow Welsh coaches Shaun Edwards and Rob Howley, will be joining McGeechan in the Lions coaching team.
"There's no bad blood there. Emotion is no bad thing in rugby - you want people to be right on the edge. You certainly do on a Lions tour," added McGeechan.
"What Warren was saying was, in fact, a back-handed compliment to Irish sides. There's nothing wrong with players squaring up to each other occasionally.
"These are the sorts of Test-match animals you are looking for. You want fighters. That's why Saturday's game in Cardiff was so encouraging. You want guys in a Lions jersey who can go right to the wire and come through."