Police in the central Indian city of Nagpur said last week they had taped conversations in which Samuels had passed on team information to a man suspected of being a bookie during last month's one-day series.
ICC spokesman Brian Murgatroyd said the governing body's anti-corruption unit was speaking to the police and cricket officials in Nagpur after being given the details by the Indian cricket board.
"The unit will extract more details and all possible angles from the police," Murgatroyd said in Nagpur on Monday. "We will leave no stone unturned in the investigation."
He stressed that no timeframe had been fixed by the ICC in which to complete the probe.
Nagpur police officer Amitesh Kumar told reporters that Samuels had five conversations with the suspected bookmaker, identified in the calls as Mukesh Kochar, from his hotel room in Nagpur ahead of the January 21 match.
Kumar said there was no evidence money had changed hands and he had only brought it to the notice of cricket authorities because it was a violation of the ICC's code of conduct, which bars players from dealing with bookmakers.
Samuels has admitted he has known Kochar for the past six years but did not believe he was a bookmaker. The Dubai-based Kochar told the Indian media he was not a bookie and that Samuels was like "a son" to him.
Cricket was embroiled in a match-fixing scandal in 2000 when New Delhi police tapped conversations between former South African captain Hansie Cronje and an Indian bookmaker during a Test and one-day series in India.
Cronje and two other former captains, Mohammad Azharuddin of India and Salim Malik of Pakistan, were banned for life.
The latest controversy comes a month before cricket's showpiece event, the World Cup, begins in the Caribbean on March 13.