Unlike his predecessor, SBI's current chairman Rajnish Kumar did not get an extension to his term, which ends on October 7 after three years.
The federal government will need to approve the Banks Board Bureau's recommendation before Khara can take the job.
Khara took up his current role, in which he oversees global markets and subsidiaries of SBI, in August 2016 for a three-year period, which was extended for another two years last year.
The Banks Board Bureau also named another SBI managing director, Challa Sreenivasulu Setty, as the candidate on the Reserve List for the chairman's job, to take the post if Khara does not.
India typically picks bosses for public sector banks from state-run lenders. These account for more than 60% of the country's banking assets, but have lagged private rivals in profitability and have amassed bad loans at a faster pace.
Mumbai-headquartered SBI reported an 81% surge in profit and better asset quality in the quarter to June as its bad loan provisions dropped. It provided a steady outlook for the coming quarters.
(Reporting by Nupur Anand; Editing by Jan Harvey)