Crs Mark Oldfield and Bronwyn Murray have filed a notice of motion asking for a vote of no confidence in Sir Kerry's chairmanship.
However, they have two hurdles to clear before it is known whether there will be a new chairman. The first is when the council meets in Timaru on tomorrow.
The 14 councillors will vote on whether to put the notice of motion on the council's agenda for its meeting on September 24 in Christchurch.
If there is a majority in support, then the no-confidence vote will take place at next month's full council meeting.
If the council passes the no-confidence motion on September 24, a new chairman will have to be elected.
In October 2007, after the local body elections, Sir Kerry and his long-time rival, Alec Neill, were tied on seven votes each for the chairmanship.
However, after a break in the council meeting, Cr Murray changed her vote to support Sir Kerry and he was elected by eight votes to six.
This time, Cr Murray is supporting the no-confidence vote.
But council insiders say the key to the no-confidence vote may be Cr Jo Kane. Cr Kane supported Cr Neill in 2007, but is now deputy chairwoman of the council.
If the notice of motion survives tomorrow, and the vote is tied on September 24, then Sir Kerry will remain chairman.