Sabina Park is undergoing a 29 million dollar facelift in preparation for the 2007 World Cup but recent cement shortages on the island have caused severe hold ups in construction.
The venue was scheduled to host a practice match on May 16, followed by the first two One Day Internationals against India on May 18 and 20 before the final Test starting on June 30.
Paul Campbell, vice-president of the Jamaica Cricket Association, said getting the venue ready for the India tour would be tough.
"As we speak there is no final decision, it was brought to our attention last week (by the Sabina venue development team) that under the current circumstances meeting the deadlines will be really, really tight.
"The focus is World Cup 2007. That's the big picture," said Campbell.
"What is being assessed is whether hosting international games in the short term will impact negatively on our hosting the World Cup next year.
"How will it affect our delivery of the venue on time? That's the question."
A decision is to be taken this week whether the games can go ahead at Sabina Park or they will be moved to another territory.
Cement shortages have also held up work on the second stadium in Trelawny on the north coast of the island which is due to host the opening ceremony of the World Cup.
Sabina Park was awarded a World Cup package that will see it hosting seven matches, including the opening game and one semi-final.
The venue development has been behind schedule almost from the inception of the project with labour problems also said to be a factor.
Additional headaches for local World Cup organisers are the likelihood of heavy rain in traditionally wet May to be followed by unpredictable weather in the hurricane months of June, July, August, September and October.