The collegium held a four-hour meeting to deliberate upon the matter after the Centre returned Court's recommendation and requested the collegium to reconsider the recommendation.
The other names will be decided on a meeting on May 16.More news: Kendall Jenner opens up about little sis Kylie's pregnancy
The elevation of Justice Joseph, who is presently the Chief Justice of Uttarakhand High Court, had run into rough weather after the Centre wrote to the Collegium on April 26 and April 30 to reconsider his name.
Apart from Joseph, the other names that the collegium considered were Indira Banerjee, now chief justice of the Madras HC, who is originally from the Calcutta HC; Gujarat HC chief justice R. Subhash Reddy, who is originally from the Telangana and Andhra Pradesh HC; and Karnataka HC chief justice Dinesh Maheshwari, who is originally from the Rajasthan HC.
According to current norms, a unanimous reiteration must be agreed to by the Centre and the Judge must be sworn in.
Reacting to the Centre's response, CJI Misra had said the government is "within its rights" to send back a name for reconsideration. Taking a cue from the May 2 agenda, sources had speculated that the collegium might consider Madras high court CJ Indira Banerjee (parent HC Calcutta), Karnataka high court CJ Dinesh Maheswari (parent HC Rajasthan) and Gujarat high court CJ R Subhash Reddy (parent HC Telangana and AP). It also questioned his seniority for elevation as a judge of the apex court.More news: Carlos Carvalhal to leave Swansea City
It is also learnt that Justice Chelameswar, who retires on June 22, has responded to all the points raised in the communication to the CJI by Law Minister Ravi Shankar Prasad expressing reservations on the elevation of Justice Joseph.
The executive remains cut up about Justice Joseph having cancelled President's rule imposed by the Centre on the state.
The Collegium at its meeting on January 10, had decided unanimously to recommend the names of Justice KM Joseph and (then senior advocate) Indu Malhotra to the Supreme Court.
"Had it been the case, why would had we approved Justice JS Khehar's name for elevation as CJI past year", he said, recalling that Justice Khehar was part of the bench which rejected the government's controversial National Judicial Appointments Commission (NJAC) Bill.More news: Trump Says 'Five Most Wanted Leaders Of ISIS Captured'