The committee, which was set up after the council passed a motion of no confidence in Mr Lowenberg, met for four hours last Friday and is due to meet again on 22 December.
An earlier date was not possible as Lord Provost Norman Irons, who chairs the special committee, had to attend a conference in Brazil this week. Mr Irons was to give an Earth Summit keynote address.
After Friday's meeting the committee issued the following statement: 'The special committee has agreed by a majority a proposal, and discussions on the basis of that proposal are ongoing and the committee will reconvene on Wednesday 22nd at 10am'. The committee split five to two in favour of putting a proposition to Mr Lowenberg's representative.