Memon had challenged the Apex court's order arguing that the legal procedure was overlooked in awarding him the death penalty.
Coverage: Yakub Memon's death sentence
The Chief Justice of India had constituted a three-member special bench to hear his plea seeking a stay on the Supreme Court order.
Memon had also filed a mercy petition before the Maharashtra Governor seeking commutation of his death sentence to life imprisonment.
Exclusive! R & AW officer who brought him back: Yakub Memon must not be hanged
Meanwhile, top Indian politicians, former judges and prominent jurists on Sunday petitioned President Pranab Mukherjee to stay the execution of Memon.
He is scheduled to be hanged on July 30.
The blasts in March 1993 ripped through Mumbai, killing at least 257 people at separate landmarks, including the Bombay Stock Exchange (BSE).
Police said Yakub Memon's brother 'Tiger' Memon and mafia don Dawood Ibrahim were the main masterminds behind the attack.