Environment Minister Jairam Ramesh has instructed officials in his ministry to complete all the work related to the issue by Friday so that a decision could be announced by that day, the source said.
The Environment Ministry had issued a showcause notice to the society on November 12, 2010, asking why the 31-storey building should not be demolished for "violating" environmental norms.
The ministry on Monday received a written reply, in which the society demanded an immediate end to proceedings against it, insisting that it had got all the required clearances.
The society has also slammed the "undue haste" shown in the initiation of punitive proceedings against it and "converting" their "meritorious case" into a "trial" by media.
The society has got caught in a controversy after it was detected that several flats meant for the kin of Kargil war victims were given to others, including politicians and top military officials and bureaucrats.