The others who were interviewed were former Durham coach Jon Lewis and Tushar Arothe, who had already served as India head coach before resigning in 2018.
The development comes days before the commencement of India's tour of Bangladesh. India were without a head coach since December last year when Ramesh Powar was sacked.
"The CAC was most impressed with Amol's presentation who was very clear in his plans for the women's team. The other presentations were good too but his was by far the best. He will most likely be recommended for the job," a BCCI official told PTI.
Muzumdar, who was most recently the head coach of Mumbai Ranji side and has had stints with IPL franchise Rajasthan Royals and South African national team, was the only one who appeared for the interview in person.
Muzumdar's first assignment will be the tour of Bangladesh, beginning July 9. India will play three T20s and as many ODIs in Mirpur.
The Indian women's team, which has often lost high-stake games from winning position in the last five years, is yet to win a world title.
Muzumdar, who is likely to get a two-year contract, will be expected to guide the team to an elusive ICC title in Bangladesh next year when the T20 World Cup will be played in September-October.
Considering India's inability to close out knock-out games, most recently in the T20 World Cup semifinal against Australia earlier this year, the new head coach's area of focus will be to improve the physical fitness of the players besides working on their mental toughness.
"Fitness is a major area of improvement for the women's cricket team. Some of the players in the national side really need to work on their fitness. Muzumdar also highlighted the need to have a full fledged support staff, including a mental trainer.
"He is fully aware of what this team needs to get to the next level," the Board official added.
The next two women's ICC events are in the sub-continent -- Bangladesh and India, and that also has gone in Muzumdar's favour.
India will host women's ODI World Cup in September 2025.
"Communication is not a problem with an Indian coach and he also has a rich experience of playing in the sub-continent conditions."
Muzumdar amassed more than 11,167 runs in first-class cricket but despite piling on the runs, he could never make it to the Indian team.