"Even Sunil Gavaskar played under me. I played under K Srikkanth and (Mohammad) Azharuddin. I had no ego," Dev, 63, was quoted as saying to the Mid-Day newspaper, referring to other greats of the era.
"Virat will have to give up his ego and play under a young cricketer. This will help him and Indian cricket. Virat should guide the new captain, new players. We cannot lose Virat, the batsman... no way."
The race to succeed Kohli is seen as a contest between Rohit Sharma and KL Rahul and -- in distant third place -- the younger Rishabh Pant, 24.
TV commentator Harsha Bhogle tweeted on Monday that Ravichandran Ashwin and Jasprit Bumrah should also be considered.
Rohit, 34, is already Twenty20 and ODI captain, and has led the Mumbai Indians to five victories in the Indian Premier League (IPL).
With Rohit injured, Rahul, 29, captained India in the recent second Test in South Africa and will lead the one-day side in the upcoming series beginning Wednesday.
The outspoken and sometimes combative Kohli's resignation stoked rumours about rifts with the sport's national governing body, the Board of Control for Cricket in India (BCCI).
Kohli and BCCI chief Saurav Ganguly in December had publicly contradicted each other over his stepping down as white-ball captain.
The Hindustan Times reported that Kohli had spurned an offer by the BCCI to quit with fanfare after his 100th Test in Bangalore in February when India host Sri Lanka.
"I think clearly there was disenchantment between Kohli and the authorities," veteran cricket journalist Ayaz Memon told AFP.
"You don't need any statement, you can sense it from the manner he gave up the T20 captaincy and then the ODI captaincy was taken away from him," he said.
He said that it will also be a challenge for the new captain to revive the team's batting fortunes from the current "crisis".
"It has become a challenging situation for India because you have a team that has crumbled, the batting certainly," he said. Arun Dhumal, BCCI treasurer, said he wasn't worried.
"I am sure with the kind of bench strength we will get over with this phase as well," Dhumal told AFP.
"It's just the change in leadership position that will happen, and when eventually somebody would take over they would take it from here and make sure the team gives its best on the field."
"Let us focus on Team India rather than thinking and bothering about what is being printed or spoken about," he added.