Gary Kirsten, who has taken over as India coach before the series against his home country, has told the Board of Control for Cricket in India (BCCI) that Singh's services will not be required, the Hindustan Times reported.
The former India all-rounder joined the team along with bowling coach Venkatesh Prasad last year following their shock first-round exit at the World Cup in West Indies.
Venky and Robin had a dispute with the board over their involvement with the lucrative Indian Premier League (IPL), due to be launched next month, the paper said. Prasad is expected to continue in his role.
The first match of the three-Test series starts in Chennai on March 26 while Ahmedabad and Kanpur will host the second and third Tests respectively.