Khan would replace Shyamala Gopinath who retires on June 20, after a seven-year stint as deputy governor.
According to sources, the finance ministry has cleared Khan's appointment for the deputy governor's post.
The proposal would now be referred to the Appointments Committee of the Cabinet, which is headed by the prime minister.
A search committee to select a new deputy governor, headed by RBI Governor D Subbarao, had suggested two candidates - H R Khan and G Gopalakrishna - for the deputy governor's post, after interviewing seven RBI executive directors last month.
If appointed a deputy governor, Khan would supersede three executive directors - V K Sharma, V S Das and G Gopalakrishna.
An RBI deputy governor can be appointed for a maximum of five years and the retirement age for a deputy governor is 62. To be eligible for the deputy governor's post, a candidate must have at least two years of service left.
As an executive director, Khan looks after four portfolios - the foreign exchange department, external investment and operations, government and bank accounts and internal debt management.
Gopinath, who looks after the foreign exchange department, is also in charge of payments and settlement, non-banking supervision, the financial stability unit and external investment and operations.
The other RBI deputy governors are K C Chakrabarty, Subir Gokarn and Anand Sinha.
RBI is also increasing the number of executive directors from seven to nine.