The bank did not disclose the names of the candidates.
Indian banking rules require private-sector banks to obtain prior RBI approval for the appointment of their managing director and CEO, giving the regulator a key role in vetting senior management.
Jagdishan, who has led the bank since 2020, is set to step down at the end of his second term in October.
The bank also moved to bolster its board, reappointing V. Srinivasa Rangan as a whole-time director, a regulatory designation for full-time bank directors, and appointing Chief Credit Officer Jimmy Tata to the board in the same capacity.
Deputy Managing Director Kaizad Bharucha is already a whole-time director.
The bank also said it would create a fourth whole-time director position, to be held by the incoming CEO once appointed.
