The fifth Test against England in Dharamsala will be the 100th Test of Ashwin's illustrious career.
Gavaskar also expects skipper Rohit Sharma to honour Ashwin with the gesture when India and England square off in the series finale from March 7.
Ashwin will become the 14th Indian cricketer to feature in 100 Tests when he walks out onto the field in Dharamsala. He made his 99th Test memorable with a five-wicket haul in Ranchi on Sunday.
Thanks to his stunning spell, India bundled out England for 145 in the second innings, which meant the hosts needed 192 runs to win the match as well as the series. At stumps, India were 40/0 with Rohit Sharma (24*) and Yashasvi Jaiswal (16*) unbeaten.
"India win tomorrow (Monday) and you all go to Dharamsala. I just hope Rohit Sharma allows you to lead the team onto the field when you take the field, that will be a gesture, wonderful honour for all that you have done for Indian cricket," Gavaskar told Ashwin when the off-spinner spoke to the broadcasters after the close of play on Day 3 in Ranchi.
While Ashwin thanked Gavaskar for bringing up the talk of the honour, he said he is happy with just playing for the national team and has no such expectations.
"Sunny bhai, you are being too generous, I have no expectations out of all these things. I am well past all that. I am enjoying every single moment being with this team. The longer it lasts, the happier i will be," Ashwin stated.
For R Ashwin, enjoying Test wins with his teammates is more rewarding than any sort of personal milestones.
"Yeah Ravi bhai, you can pick all the wickets you want, you can set all the records you want. But nothing can match the feeling of a team win. So yes, winning a Test match at the end of 4-5 days, the feeling is surreal. I want that feeling tomorrow. Ro and Jaiswal have started really well, I hope they can continue well tomorrow," he remarked.