Sportal.co.nz 27.Apr.2013Getty Images
The squad, which consists of players from England, Ireland, Scotland and Wales, will head to Australia for June's three-match Test series with head coach Warren Gatland looking to mastermind an end to a 16-year Lions' drought.
McGeechan was in charge when the Lions last claimed overall success on Tour in 1997, with a 2-1 victory over South Africa.
But the former Scotland second five-eighths is concerned the squad will not be given enough time to prepare properly for the rigours of the tour, which includes seven non-Test matches.
The Premiership and Pro12 competitions end on May 25 - just 24 hours before the Lions depart for their 125th anniversary tour. It is the shortest lead-in time for any Lions tour in history.
"For the players, the Lions is the biggest jersey they can wear," McGeechan said.
"All I would like to see is rugby administrators giving them the best fighting chance with an extra week's preparation.
"If you've got a team that go halfway around the world and take 35,000 people with it to support it, then in the year it exists it's the biggest team in world rugby.
"It's bigger than the All Blacks, it's an absolute phenomenon."
Gatland will announce his squad on April 30 and McGeechan, who led the Lions for three tours and played for them on two, reckons the New Zealander will be up against it when preparations finally get underway.
"The first two or three weeks will be critical in Warren Gatland being able to get all the players together and on the same wavelength," McGeechan added.
"By week five, you are looking at preparing for a Test match. My philosophy was to give every player the opportunity to show what he can do in a Lions jersey so they have to be playing in those first four weeks."