Labour leaders may ask their members for their views on any deals with other parties after the Welsh assembly election left no clear winner.
Labour is still the biggest party with 26 seats, while Plaid Cymru went up to 15, Tories rose to 12 and Lib Dems stayed at six, with one independent.
Labour seems certain to seek the support of rivals before forming the next assembly government.
All the parties are examining the new political landscape after Thursday's election.
Leaders have been talking to their parties about possible coalitions or deals.
Some in Labour think that rank-and-file members should be consulted before entering any deal and the decision should not just be left to AMs.
The voters of Wales gave no party an overall assembly majority
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It is possible that if Welsh Labour leaders did decide to consult the membership, it would have to call a special party conference.
A decision will have to be made quickly, because the make-up of the next assembly government and the first minister would have to be settled by 24 May at the latest. The new first minister will be sworn in by the Queen on 30 May.
Meanwhile, there could also be opposition among Lib Dems towards reviving a coalition with Labour.
The Lib Dem constitution also stipulates that the leadership has to consult its members before a deal.
Plaid leader Ieuan Wyn Jones said it was obvious that Wales needed a stable government and he agreed with Mr Morgan that ruling with only 26 seats was "not sustainable".
'Desire to change'
Mr Jones said there could be "a formal coalition, or a less formal coalition, or a written agreement which delivers a programme".
Nick Bourne, leader of the Conservatives in the assembly, said Labour's hold on power had been "seriously weakened," and indicated that Tories could play a part in a coalition.
"The onus is now on political leaders from all parties to form a government which will provide stability for the next four years," said Mr Bourne.
"Political parties with a real desire to change Wales for the better need to set aside their differences and work together in the interests of everyone in our country."
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The Politics Show team on Sunday 06 May 2007 at 12:00 BST on BBC One.
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