Rahul, along with South African cricketer Wayne Parnell, was detained by police after being caught in a rave party in Mumbai during the Indian Premier League in May. The two were among 42 people who tested positive for drugs, the Mumbai Police said yesterday.
With two specialised spinners R Ashwin and Pragyan Ojha in the team, Rahul was not an automatic choice in the playing XI in any case.
The BCCI will, however, take action against the young spinner only after studying the police report on the matter.
"The Police report will be studied before taking any action against Rahul Sharma," Senior BCCI official and IPL Chairman Rajeev Shukla said today.
"Only after studying the report we will proceed," he added.
The BCCI officials have sought a detailed report from the Mumbai police authorities and will take a final call on whether to withdraw Rahul from the team at a later stage.
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Mumbai Police said Rahul and Parnell were among the 42 who tested positive for drugs. The two cricketers were among the 100-odd people who were detained on that day.
"I don't know why everyone is in a mood to execute Rahul Sharma without even going into the details," Srinivasan had told PTI last night.
"The BCCI will first procure each and every bit of relevant information and then study them before deciding on the course of action," he added.