With Kohli going on paternity leave after the opening day-night Test against Australia in Adelaide, Rahane is expected to lead the team in the remainder of the four-Test series.
"There is no real pressure on Ajinkya Rahane, because both the times that he has led the team, he has won. He led against Australia at Dharamshala and India won. He led against Afghanistan and India won," Gavaskar said during Star Sports show 'GAME PLAN'.
"So, as far as his captaincy is concerned, there is going to be no pressure because he knows he is at the moment, only the stand-in captain for the 3 Test matches.
"So, I don't think the fact about being a captain or carrying on as captain is going to be part of his thinking at all."
Rahane had captained the side during the two warm-up games which ended in draws.
"He will do the job as honestly as he plays his cricket, which means, as a batsman, he will go out there and try and let Pujara try and grind the opposition in and play few more shots maybe," Gavaskar said.
Batting mainstay Cheteshwar Pujara was adjudged Player of the Series for scoring 521 runs in the 2018-19 series that India won 2-1 and Gavaskar feels he will once again have to bat for long periods if India have to do well in the upcoming rubber.
"Out of 20 days of Test cricket that we have ahead of us, we are really happy to have him bat for 15 days, there is no question about it," he said.
"Whether he has played any cricket or not, I don't think it’s going to make any difference because he is so strong mentally.
"... He loves batting, he loves being at the crease, he loves wearing the bowlers down. In the last two years, he has also improved his strokes and range of shots."
Former Australia opener Matthew Hayden too showered praise on Pujara.
"... he hurt us badly. We are of a generation now where we are admiring people for their stroke play, we are admiring people for their strike rate. Well, he is one of the few guys in Test cricket that have a strike rate of sub 45 and he can hurt you."
The opening Test begins at Adelaide on Thursday.