The governor of Maharashtra state has also turned down his mercy plea.
His last hope is a clemency plea pending before the president who rejected a similar petition last month.
The serial blasts killed 257 people and were allegedly to avenge the killing of Muslims in riots a few months earlier.
Earlier, the Maharashtra state authorities had set his execution for Thursday morning and Indian media reports say unless President Pranab Mukherjee intervenes, Memon will be hanged.
India rarely sentences people to death - and even more rarely carries out executions. There have been three since 1995.
If the hanging goes ahead, Memon will be the first person to be executed since a Kashmiri man, Afzal Guru, was hanged in 2013 for the 2001 attack on the Indian parliament.
Memon, a chartered accountant, was sentenced to death in 2007 by a special court in Mumbai, which found he played a key role in the bombing conspiracy.
He is being held in a prison in the western city of Nagpur.
On Wednesday, Supreme Court judges rejected Memon's plea which said the government did not follow proper legal procedures in issuing the warrant for his death.
Authorities in India say Memon's brother, Tiger Memon, is believed to have played an instrumental role in carrying out the attacks.
Yakub Memon's case has divided opinion in India, with many asking for the suspension of the death sentence.
Politicians, social activists, journalists and lawyers recently urged the president to commute the sentence and "spare him from the noose of death for a crime that was master-minded by someone else to communally divide India".
India's Supreme Court has turned down a final plea for reprieve by Yakub Memon, convicted of financing the deadly 1993 Mumbai bombings, clearing the way for his execution.