Gill has travelled with the squad to Guwahati but faces a race against time, with a decision set to be made late on the eve of the match.
The top-order batsman suffered neck spasms in the first innings of the opening Test and pulled out of the remainder of the match, spending a night in hospital.
"He is definitely recovering really well," batting coach Sitanshu Kotak said on Thursday, amid reports in Indian media that Gill is set to miss the Test.
"The decision will be taken tomorrow evening because the physios, doctors will have to take a call that even if he is fully recovered he should not get the spasm again during the game."
"If he is fully recovered and it is a guarantee that he won't have this issue again then he will play," said Kotak.
"If there is doubt, then I am sure he will take rest (for) one more game because it won't be helpful to the team."
India lost a low-scoring first Test in Kolkata inside three days after they failed to chase down 124 on a turning pitch with inconsistent bounce.
A batter short with Gill out, India were bundled out for 93 to trail the two-match series 1-0.
Kotak said the hosts have a strong bench to fill Gill's spot if the captain does not play.
"A player like Shubman and a captain any team would miss, but if he is missing out due to injury we have batters and plenty of good players," he said.
South Africa, led by Temba Bavuma, are chasing a first series win on Indian soil since Hansie Cronje's team triumphed there in 2000.
