The sources added that Murmu is set to be the next Comptroller and Auditor General of India (CAG) taking over from Rajiv Mehrishi, who will retire this week.
While reports said Murmu has sent his resignation to Kovind, there is no confirmation whether it has been received by the President and if it has been accepted or rejected.
Murmu was appointed as the first L-G of Jammu and Kashmir last October after the formation of the new Union Territory under the Jammu and Kashmir Reorganisation Act, 2019.
Earlier on Wednesday, Army commander of Northern Command had called on Murmu and discussed the overall security management of the Union Territory.