Although the Scotland fly-half is still in the early stages of recuperation, he is no longer wearing a surgical boost and could return to full training by the end of next week.
The first Test takes place in Cape Town on July 24, with the second and third scheduled for July 31 and August 7.
“We’re now five to six days into his recovery,” said Townsend, the Lions attack coach. “He’s had an injection into that area and he is out of his boot so he’ll start the rehab process gently this week and then when we get to the end of the week we’re hoping he will be able to be back involved in full training.
“It’s unlikely he will be involved in the first Test but we’re still hopeful he will be involved in the last two.”
Russell was the starting stand-off in the opening tour match against the Sigma Lions and then came off the bench in the first game against the Sharks in Johannesburg. He was forced to withdraw from the squad for the second match against the Sharks because of the Achilles problem.
England’s young stand-off Marcus Smith has been called into the Lions squad as cover.