Webster sustained bruising to his lower leg and ankle and went off early on in Scotland's 44-15 defeat by Australia, despite scoring a try after the injury.
The 25-year-old has been running in the swimming pool after taking off a protective walking boot at the weekend.
However, a neck problem has ruled Andrew Easson out of Saturday's Heineken Cup pool match at Gloucester.
Meanwhile, Simon Cross has been loaned out to struggling English National League One club Waterloo to increase his match fitness.
The flanker will return to Edinburgh before the Magners League registration deadline at the end of January.
The 25-year-old joins Ander Monro, who has gone to the Merseyside club on loan until the end of the season.
Cross said: "I'm delighted to be getting some game time. It's really a means to an end so that when I return I'll be match-fit and ready to play for Edinburgh.
"It's a great opportunity to get some rugby under my belt after a torrid start to the season injury-wise.
"I've got connections with Waterloo as I was at school with the son of Malcolm Boucher who works at the club and my sister was also at school with his daughters.
"I'm looking forward to getting back together with Ander and working with the guys at Waterloo."