Mr Dutton's supporters have been circulating a petition to bring on another partyroom meeting on the issue of the leadership.
Mr Dutton himself earlier admitted he had been consulting with colleagues.
Today ((aug 23)) is the last day federal parliament sits until September the 10th, with the next partyroom meeting scheduled for September the 11th.
Liberal backbencher Stuart Robert admits there will likely be a second ballot for the leadership, either today ((9aug 23)) or in the near future.