In the letter, the left-wing rebels from the eastern state of Jharkhand and neighbouring Chhattisgarh also decided to kill top cricket officials Sharad Pawar, Niranjan Shah and Rajiv Shukla, according to the Hindustan Times.
"All five are promoting cricket -- a sport of the elite class -- and also leading a luxurious life at the expense of the hard-earned money of the common man," the newspaper quoted the letter as saying.
Pawar is president of the Indian cricket board and federal minister for agriculture.
Jharkhand Chief Minister Madhu Koda said the letter was being taken seriously and Dhoni's security would be reviewed if necessary.
"But before providing more security to Dhoni, the government would like its agencies to find out whether the letter is genuine," he said.
Wicketkeeper-batsman Dhoni, who hails from Jharkhand, and skipper Dravid are currently on tour for India's second and final Test against Bangladesh in Dhaka.
The paper said the handwritten letter, suspected to be an internal communication, was found during a raid on a rebel hideout in Dantewada region in Chhattisgarh on Friday.
In March, 55 policemen were killed by Maoists in Chhattisgarh in one of the worst-ever attacks on Indian security forces.
It followed the assassination of high-profile federal member of parliament Sunil Mahto by Maoists in Jharkhand on March 4. He was the first national-level politician to be assassinated by the left-wing rebels.
The Maoist insurgency began in the 1960s in India as an armed peasant movement. The rebels, who say they are fighting for the rights of landless farmers, operate in 15 of India's 29 states.