Union Water Resources Minister Saifuddin Soz said under the final award given on February 5, there is a three-month period during which parties concerned can approach the Tribunal for a review.
After the parties challenge the verdict, there will be hearings by the Tribunal which could take up to one year, he said.
"We can notify the award only when the entire process is over," Soz said.
The Tribunal, which allocated 270 tmc ft of water to Karnataka, has directed it to ensure release of 192 tmc ft to Tamil Nadu annually, which gets 419 tmc ft as its share.
Both Tamil Nadu and Karnataka, which are at loggerheads over sharing of the common river water, have expressed dissatisfaction over the Tribunal's award and decided to seek a review.
Opposition AIADMK in Tamil Nadu has, however, demanded immediate notification of the award.
The Cauvery issue is expected to generate much political heat in Parliament in the coming days as Lok Sabha Speaker Somnath Chatterjee has convened a meeting of MPs belonging to Karnataka and Tamil Nadu tomorrow.
The meeting is expected to decide on the format and date of discussion in Parliament, a move which has been vehemently opposed by Tamil Nadu Chief Minister and DMK supremo M Karunanidhi.