Shaw has just been released by London Wasps after they decided not to renew his contract but the 37-year-old is thought to be considering playing on for one more year elsewhere.
And the Mail on Sunday and Daily Mail are reporting that McGeechan is interested in bringing Shaw to Bath for a final season's swansong before the giant second row calls time on an illustrious career.
Shaw had first been heavily bombarded with questions of retirement the year before the 2009 Lions tour but his determination to be part of the trip to South Africa ensured he continued fighting the odds despite being written off by plenty of critics.
Shaw's professionalism, experience and consistently high levels of performance throughout 2008/09 meant it was far from a surprise when McGeechan picked him for what was his third Lions tour.
And Shaw repaid his then Wasps boss in the best possible fashion with two outstanding Test performances in the second and third internationals in the Republic as the Lions came within a whisker of toppling the World Champions.
A Lion first time around in 1997, Shaw was the only player from that triumphant tour to return to the country with Britain and Ireland's elite 12 years later. He missed out on selection for the 2001 adventure in Australia but was called up as a replacement for the 2005 tour to New Zealand.
But it was in 2009 that Shaw really left his Lions legacy as he was named man of the match in the heart-breaking 28-25 reverse to the Boks in Pretoria in what proved to be the decisive rubber.
Currently training with England as Martin Johnson's men prepare for the World Cup, Shaw, who turns 38 in September, could move to Bath for the start of the new season if he is one of the unfortunate 15 to miss the cut for the final 30-man squad.