''The five-star hotels are very expensive,'' Speed told BBC Sport.
''I hope when I go back there in August to the quarterly board meeting of the Cricket World Cup organising committee that we'll have some good news,'' he added.
Mr Speed said awarding the World cup rights to West Indies was a ''brave decision'' by the ICC but added that he was expecting a good time in keeping with the Caribbean way of life.
''At my first ICC meeting in 1997, the ICC members granted the World Cup to West Indies. I remember thinking at the time, That's a very brave decision I'll watch with interest the World Cup in 2007, without realising I would be chief executive at that time,'' he recalled.
Satisfied with the progress of work so far, the ICC chief executive appreciated the coordination between the organisers and the governments of all nine participating nations.
''There are nine islands involved, so nine grounds and 20 practice venues are being built for major matches. They are all being funded by the various governments of the West Indies so they're all right behind it,'' he explained.
''I think it will have a particularly West Indian favour and I think it will be great fun,'' he added.
However, Mr Speed was concerned about the hurricane season in the islands, whih will be there for the remainder of the year, and said he would be happy to see nature's fury die down without causing any significant damage to the newly-built infrastructure.
''We have to get through another hurricane season over the next three or four months - some of the grounds have had problems with hurricanes,'' he said.