The newspaper said it had uncovered evidence that tens of thousands of pounds (dollars) was on offer to players to throw part or all of international matches, including last year's World Cup semi-final between India and Pakistan.
It cited one Delhi bookmaker boasting that English county cricket was also a "good new market", as it involved "low-profile matches and nobody monitors them. That's why good money can be made there without any hassle".
The allegations come just weeks after former Essex bowler Mervyn Westfield became the first English cricketer to be jailed for corruption after admitting accepting money to fix a match against Durham in September 2009.
An ICC spokesman said it would investigate the new allegations.
"We are grateful for the information you have provided and will launch an inquiry into these serious allegations," he told The Sunday Times.
"Betting on cricket in the legal and illegal markets continues to grow rapidly and, with many, many millions of dollars being bet on every match, the threat of corrupters seeking to influence the game has not gone away."