The former Brexit negotiator Oliver Robbins is one of 10 applicants on the longlist to take over from Simon Case as the UK’s most senior civil servant, the Guardian understands.

The candidates, who have their first round of interviews for the job this week and next, are predominantly internal applicants, with several permanent secretaries believed to have thrown their hats into the ring.

Whitehall sources said several senior external female candidates who had previously been linked to the post had decided not to apply, prompting concerns in Downing Street as the job of cabinet secretary has only ever been held by white men.

One source said Robbins was the probable favourite but that the permanent secretaries Tamara Finkelstein, Sarah Healey, Antonia Romeo, Jeremy Pocklington and Peter Schofield were all credible internal contenders.

Sir Suma Chakrabarti, who was a permanent secretary in the justice department while Starmer was director of public prosecutions, is also believed to have been considered despite having been out of the civil service for a decade.

Starmer appointed Jonathan Powell, Tony Blair’s former chief of staff, as his national security adviser last week. Sources said the prime minister wanted the best person to take over from Case, but he may be uncomfortable about appointing two men in quick succession for senior roles.

Sources said Minouche Shafik, a former permanent secretary at the Department for International Development who recently stepped down as principal of New York’s Columbia University over its handling of protests about Gaza, had not applied for the cabinet secretary role.

Melanie Dawes, Ofcom’s chief executive, who was the permanent secretary in the communities department at the time of the Grenfell Tower fire, is also understood not to have thrown her hat into the ring for the job.

Sharon White, the former Treasury number two who recently stood down as chair of the John Lewis Partnership, ruled herself out at the formal launch of the recruitment campaign.

Instead, she is sitting on the Civil Service Commission recruitment panel that is vetting candidates. She is joined by the former cabinet secretary Gus O’Donnell; the Ministry of Defence lead non-executive director, Brian McBride; and first civil service commissioner, Gisela Stuart.

Sources said Tom Scholar, who was sacked as Treasury permanent secretary by Liz Truss days after she became prime minister, had no interest in running for the job. “He’s long gone,” said one. The next round of interviews will take place in early December.

Robbins, who was recently made a partner at Hakluyt, a consultancy founded by ex-MI6 intelligence officers, has repeatedly been linked with the job. He oversaw Brexit negotiations under Theresa May before leaving the civil service in December 2019.

He was thought to be the preferred choice of Sue Gray, Starmer’s former chief of staff. However, some within No 10 are keen for someone with less Brexit-related baggage and would prefer a less obvious candidate – especially given the long history of white male cabinet secretaries.

The other external candidates for the role are understood to be former permanent secretaries with little or no media profile. “Not box office,” said one insider, suggesting the prime minister would prefer a cabinet secretary who is not in the public eye.

Others within Whitehall who have been tipped are Tamara Finkelstein, the permanent secretary at the Department for Environment, Food and Rural Affairs; Jeremy Pocklington, who runs the Department for Energy Security and Net Zero; and Antonia Romeo, the senior civil servant at the Ministry of Justice.

Alex Thomas, a programme director at the Institute for Government, said: “It looks like it’s still a wide field and the decision will be Keir Starmer’s to make, which means it’s hard to predict.”

Case announced in September that he would stand down at the end of the year on health grounds. In an email to the civil service, the top official – who has served four prime ministers and 120 cabinet ministers in the role – said he would stay in post while the process to replace him began.