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 have to seek the support of rivals before forming the next assembly government.
Some Lib Dem party members threatened to quit if there is a deal with Labour.
All the parties are examining the new political landscape after Thursday's election.
Leaders have been talking to their parties before discussions with rivals about possible coalitions or deals.
A renewed Labour coalition with the Liberal Democrats seems the likeliest option, although that is not certain. But a so-called "rainbow alliance" of Plaid, Tories and Lib Dems is also a possibility.
However, 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.
Labour was in coalition with the Lib Dems from 2000 to 2003 for part of the assembly's first term.
It is possible that if Welsh Labour leaders did decide to consult the membership, it would have to call a special party conference.
The voters of Wales gave no party an overall assembly majority
Welsh Labour leader Rhodri Morgan said his AMs would have "a free and open discussion within the group on what's the best way forward".
He said: "It's not a question of taking your bats home because you have not got a majority. You have got to deliver for the people of Wales."
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 six Lib Dem AMs will meet on Saturday amid reports that some party members are threatening mass resignations if they again team up 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.
"Welsh Conservatives are willing to play our part in that to ensure that the new assembly government delivers for the people of Wales. We call upon all those who share our beliefs to work with us to achieve this goal over the next four years."
Newly-re-elected Lib Dem Peter Black has also indicated his unhappiness with the state of his party after winning six seats for the third consecutive assembly election.
He wrote on his weblog: "This is not healthy and it is clear that we now need a fresh approach and a radical re-think as to where we are going and how we sell ourselves, our policies and our philosophy to the Welsh electorate."
Mr Black told BBC Radio Wales later that leadership decisions were for the whole party to make but refused to rule out the possibility, saying change "had to be looked at."
The new assembly will sit for the first time next Wednesday, 9 May.