The world's largest coal miner produced an average of 1.34 million tonnes during the first 22 days of April, the source said, down from 1.51 million tonnes per day April 2019.
It produced 2.72 million tonnes per day on average in March.
The source did not wish to be identified given the sensitivity of the matter. Coal India did not immediately respond to an email seeking comment.
Coal minister Pralhad Joshi said on Thursday the state-run miner is targeting production of 710 million tonnes, or 1.94 million tonnes per day, during the year ending in March 2021.
That is 17.9 per cent higher than its 2019/20 output of 602.1 million tonnes.
The company's annual production fell in 2019/20 for the first time since 1998/99 as the heaviest rainfall in 25 years battered coal mining regions and a broad economic slowdown stifled demand.
Lower demand due to a nationwide lockdown to prevent the spread of the coronavirus has created record high fuel stocks at utilities, Coal India's biggest clients, prompting many power plants to avoid buying more coal, officials say.
Electricity consumption has fallen 24.3 per cent compared with last year during the nationwide shutdown India started on March 25, an analysis of government data showed.
India's electricity generation from coal-fired utilities fell for the first time in 2019, a phenomenon industry executives say could become a trend in 5-10 years.