The veteran second row was one of the stars of the 2009 Lions tour of South Africa and his form on that tour could see him make a permanent move to the Republic.
The 36-year-old London Wasps stalwart is being lined up by the Golden Lions Rugby Union for the 2010 season as the Johannesburg-based side look to improve their fortunes following recent disappointments.
The Lions have recently announced the signing of Springbok wing Tonderai Chavhanga from Western Province and are desperately trying to hang on to star centre Jaque Fourie, who is in the middle of an arbitration hearing against the union as he attempts to move in the opposite direction.
Shaw, who starred in both the second and third internationals against the Springboks this summer, made a real impression for Ian McGeechan's men as he helped the Lions come so close to securing a series win over the World Champions.
The former Bristol University student was the only surviving squad member from the 1997 tour of South Africa but initially missed out on Test selection as the Lions began the three-match series with defeat in Durban.
With the Lions having struggled in the physical exchanges at the ABSA Stadium, Shaw earned a call up to the starting XV for the second Test at Loftus Versfeld. The Lions may have again lost out but, like the team as a whole, Shaw did his reputation no harm whatsoever with a stunning man-of-the-match display.
Ironically, the Golden Lions were one of only two provincial sides Shaw didn't play against on the 2009 tour - the other being the Cheetahs.
If Shaw does move to South Africa next year, it will signal the end of a lengthy association with Wasps. The Kenyan-born England international joined the now Adams Park outfit from Bristol in 1997 and has spent the past 12 years with the club.