The event is the brainchild of the Texan billionaire Allen Stanford, who is hoping to draw world champions Australia, Sri Lanka, India and South Africa to the inaugural week-long series proposed for June 2008.
ICC chief executive Malcolm Speed said in a statement its Board discussed the idea at its recent meeting in London.
"Our members have raised genuine concerns about the concept and have asked the ICC to act as an intermediary and help manage discussions between Mr Stanford and the potential host of the matches, the West Indies Cricket Board (WICB).
The event would feature a knockout event with the winners facing the Stanford Super Stars, an all-West Indies XI comprising the best players from the inter-island Stanford 20/20 tournament, due to be staged in Antigua early next year.
Stanford said last week some issues still needed to be sorted out over the event, which is subject to approval from the WICB, the ICC and its official broadcast network ESPN Star Sports.
"The members recognise the potential benefits of the tournament for the development of cricket in the West Indies," Speed said.
"At the same time they wish to ensure that their participation in any event such as this will benefit as many of the game's stakeholders as possible to help facilitate its continuing strong growth.
"The key is to achieve a result that is in the best interests of the game as a whole and, to that end, discussions will continue ahead of the ICC Board's next meeting, set to take place in Dubai in late October."
The national boards also want ICC's Future Tours Programme for bilateral series, player workload concerns and the current cap on Twenty20 internationals to be taken into consideration.
Stanford has also announced he is giving West Indies cricket $100 million over three years with most of the funding going towards grassroots development.
