The India Cricket Board has advertised the vacancy since early May as Dravid's contract expires at the end of June. The former India captain took over the national team following the 2021 Twenty20 World Cup, replacing Ravi Shastri.
"I've really enjoyed coaching India, and I think it's a truly special job to do. I've enjoyed working with this team, and it's a great bunch of boys to work with," Dravid said ahead of Wednesday's match with Ireland.
"Unfortunately, just the kind of schedules (that are in place in international cricket) and where I find myself in this stage in my life, I don't think I'll be able to re-apply (for the position)."
Former India opener Gautam Gambhir, who has been the mentor of Indian Premier League champions Kolkata Knight Riders, is a strong contender for coaching the national team, according to Indian media.
India, who have not won the Twenty20 World Cup since its inaugural edition in 2007, face Pakistan on Sunday and tournament hosts USA three days later in New York.