Lord Justice Rix and Lord Justice Dyson have been considered for the job, but it is understood that both have been rejected by the selection panel, which is chaired by the president of the Supreme Court Lord Phillips of Worth Matravers.
It is believed the preference is to appoint a chancery judge to the role, which has been vacant since the court opened in October.
Lloyd LJ was made a High Court judge in 1996 before joining the Court of Appeal in 2005.
Lord Justice Laws and Lady Justice Arden are also frontrunners. “They’re both intellectual heavyweights who’d be ideal for the job,” one barrister said.
Another source said those who had applied but had not been selected have been told. The Supreme Court declined to comment until the selection process is over.
The selection panel intended to make the decision before the end of the year to relieve pressure on the court’s timetable, but the announcement will now be made in the New Year.
Sumption had been widely tipped for the top job, but the Court of Appeal judiciary were opposed to someone with limited experience being elevated into a leading judicial position.
Last Wednesday (9 December) Sumption’s set Brick Court Chambers released a statement confirming that he was a candidate but that he had “withdrawn” his application.