The governing body's executive board will discuss the claim from the Global Cricket Corporation (GCC) following this year's tournament in South Africa.
The GCC, which was responsible for selling the tournament's marketing and broadcasting rights, is claiming around $80 million in lost revenues after two matches failed to go ahead, according to a source within the ICC.
England refused to play their World Cup game against Zimbabwe in Harare over security concerns, and New Zealand boycotted their game in Kenya for the same reasons.
India's players, meanwhile, refused to sign playing contracts tying them to the official World Cup sponsors, arguing that they already had personal deals with rival companies.
The ICC is expected to contest the claim, which could lead to long-running legal action.
The ICC, anticipating such a claim, held back millions of dollars in tournament fees from several teams after the World Cup in South Africa.
An ICC news conference will be held on Thursday.
Ehsan Mani of Pakistan, who is taking over from Malcolm Gray as ICC president, is also due to give an address on the state of the game on Thursday.
