The Scotland stand-off suffered an Achilles tear early in the tour, sparking fear that he may have to return home early.
However, Russell is making good progress and is in the mix for the match in Cape Town this Saturday.
The Lions coaches are due to have a selection meeting on Monday evening.
Warren Gatland’s side won the first Test 22-17 at the weekend and would clinch the series with another victory.
Dan Biggar was the starting stand-off last Saturday but suffered a head knock. He is now going through the return to play protocols.
“All being well, Dan should be available to train on Thursday with the team,” said Steve Tandy, the Lions defence coach.
“Finn is starting training with us today. He could potentially be in the mix [for the second Test]. We’ll see how he pulls up. I know he has been reacting well to the training so we’ll discuss all that this evening.”
Tandy also revealed that Welsh prop Wyn Jones is a major doubt for the second Test. The loosehead was originally named in the team for the first Test but had to withdraw on the day of the game due to a shoulder injury, with Rory Sutherland replacing him in the starting line-up.
“Wyn Jones has got a minor shoulder injury so he’s probably going to be doubtful for the Test match,” added Tandy.
While pleased with the win, Tandy said there was still room for improvement.
“We’ll have a debate tonight in and around selection,” he said. “We’ll talk about the game and probably focus more on where we can get better as a team going into the second Test match.
“To be fair, there was lots of good performances, and probably lots of areas we can improve on. So, we’ll probably debate selection a little bit more tonight.”
One area up for debate is sure to be the centre pairing, with Scotland’s Chris Harris a candidate to come into the team at 13 at the expense of Elliot Daly, and Bundee Aki and Owen Farrell also in the mix to start.
Tandy was reluctant to go into too much detail but acknowledged that competition for places was fierce.
“There’s lots of good things around Elliot,” said the defence coach. “There’s bits and pieces from everyone we can tidy up. Where we are as a squad at the moment, you look at Chris, you look at Bundee, you look at Faz, there’s competition right across the board.
“So, we’ll talk about selection tonight, but the second half performance of the group shows us where we can get to, and we’ll probably speak more about that tonight.
“The way the boys have performed in training, the way they have perform in previous games, I don’t think it is going to be easy tonight when we talk about selection because you’ve got lots of form from the boys who weren’t involved, but we’ve also just won a Test match in South Africa, so it will be just as difficult [as last week] tonight.”