The computer science expert, who has worked for the technology giant for 22 years, is tipped to take over the hot seat after current chief Steve Ballmer announced last August that he was to step down.
Mr Nadella is currently in charge of Microsoft's cloud and enterprise division. The company would not comment on the reports.
His appointment would end speculation that previously saw Ford boss Alan Mulally linked to the role, which Mr Mulally has quashed.
The move is thought likely to disappoint Wall Street investors keen to see an outsider brought in to institute a shake-up following Mr Ballmer's departure.
But it is thought that Mr Nadella will be welcomed among rank-and-file staff where he is seen as popular and consensus-driven.
Born in 1967 and a native of Hyderabad, he started his career at Sun Microsystems before joining Microsoft in 1992.