Gavaskar made the comments after Virat Kohli announced that he would step down from T20 captaincy after the World Cup. Rohit Sharma is set to take over from Kohli.
"It's a good thing that the BCCI is looking ahead. It's important to think ahead," said Gavaskar on Sports Talk.
"If India are looking to groom a new captain, then KL Rahul can be looked at. He has performed well. Even now in England, his batting was very good. He has been performing well in IPL and 50-overs cricket as well at the international stage. He can be made vice-captain."
Rahul captains Punjab Kings in the IPL.
"He has shown very impressive leadership qualities in the IPL. He hasn't let the burden of captaincy affect his batting. His name can be taken into consideration, added Gavaskar. Virat Kohli on Thursday announced he will step down as India's T20 skipper after the T20 World Cup in UAE but will continue to lead the side in ODIs and Test cricket, a decision that paves the way for Rohit Sharma to captain in the shortest format.
"I've decided to step down as the T20 captain after this T20 World Cup in Dubai in October," the 32-year-old Kohli, who is here to compete in the IPL that resumes on Sunday, said in a statement posted on his Twitter page.