India are due to arrive on May 15 and will play five one-dayers before the first Test in Antigua on June 1.
Their request appears to have caught the West Indies Cricket Board by surprise.
"We've requested the West Indies Cricket Board to drop one Test from the itinerary," said Shashank Manohar, head of the board's fixture committee.
WICB boss Roger Brathwaite said he hadn’t been told of the request and that it would be difficult to make changes.
Manohar, a vice-president of the BCCI, also revealed that India will play in a triangular series in Sri Lanka in August, with South Africa the third team.
India has also recently threatened to withdraw the team from future Champions Trophy tournaments, and is due to discuss the matter with governing body the ICC.
India host this year's tournament in November and December but were thought to be opposed to the bi-annual event, believing it was played too frequently.
