A cross-party committee has been established to decide whether to take no further action, give an informal warning or if further investigation is required.
Meanwhile Council Leader Terry Fox says it’s “business as usual” although there are no details about whether anyone is standing in for the CEO role.
He said: “I completely understand the strength of feeling that has been expressed in the city since Kate’s statement and apology on January 14.
“We have set up a committee to establish the facts of what has happened. While we cannot know how long it will take, we expect this to move at pace. I will be handing the process over to members of the panel, and we now need to let them carry out this work.
“I want to reassure everyone that business continues as usual for the council, and we remain focused on delivering for Sheffield.”
The committee, which is meeting in private, is chaired by Deputy Council Leader Julie Grocutt, with Liberal Democrat Leader Coun Shaffaq Mohammed, Lib Dem Deputy Leader Penny Baker, Green Party Leader Douglas Johnson and Labour councillor Sioned-Mair Richards.
It will meet again on Thursday, January 27 and on Monday, January 31. It is not due to report back until after senior civil servant Sue Gray has completed her investigation into alleged Covid rule breaking in Downing Street.
Ms Josephs released a statement and apologised about the party just minutes before a national newspaper published the story.
She had repeatedly denied to local journalists that she had been involved in any Downing Street parties.
Her statement said she had gathered with colleagues that were at work that day but it was later revealed an email was sent to 40 guests.