Aiken planned to step down at or around the company's 2021 annual meeting after six years in the post, the report said, citing sources.
Balfour, one of the contractors on the HS2 high-speed rail link, has appointed Egon Zehnder, a global management consulting and executive search firm, to begin looking for a new chairman, the report said.
Balfour Beatty company declined to comment.
Aiken joined the firm in 2015 at a time when the group had announced a string of profit warnings and rejected merger approaches.
(Reporting by Aishwarya Nair in Bengaluru; Additional reporting by Sucharita Ganguly; Editing by Chizu Nomiyama and Grant McCool)