This is the collegium's second meeting after Law Minister Ravi Shankar Prasad sent back Justice Joseph's name and asked the judges to reconsider their choice.
The government had cleared the other recommendation, Indu Malhotra, but said Justice Joseph - the chief justice of the Uttarakhand High Court - was not senior enough for the promotion. The government also said Justice Joseph is from Kerala, which was already represented in the Supreme Court.
Law Minister Ravi Shankar Prasad has denied that the centre's decision had anything to do with Justice Thomas's 2016 verdict cancelling president's rule in Uttarakhand, which enabled the Congress to remain in power.
At its meeting last week, the country's five top judges had decided to draft a point-by-point rejoinder to the centre's objections to their choice. But it also discussed names of judges from three other high courts in view of what the court called, was the "concept of fair representation".
Chief Justice of India Dipak Misra's decision to convene today's meeting came just a day after Justice Jasti Chelameswar, who ranks after him and retires soon, wrote to him. The letter sought an early meeting of the collegium and said that the judges must be firm on their choice.
But it is rare for the government to return a recommendation for elevation to the Supreme Court. The only occasion when such a situation arose in recent years was when the NDA government blocked elevation of senior lawyer Gopal Subramanium in 2014.
The then Chief Justice RM Lodha, however, could not pursue the case because Gopal Subramanium withdrew his consent to be a judge.
If the collegium sends back a name a second time, the centre has no choice but to accept it. Already the Supreme Court is down to 24 judges as against the strength of 31, sanctioned by Parliament. Five more judges are slated to retire this year.