Basque premier Juan Jose Ibarretxe will present his plan for a "status of free association" with Spain to the national parliament in Madrid later on Tuesday, but the debate is likely to end in rejection by a wide margin.
El Pais newspaper said Prime Minister Jose Luis Rodriguez Zapatero would offer a revision of the existing statute on Basque autonomy - one which respected the constitution and enjoyed broad support in the divided region.
Newspaper ABC said Zapatero would seek a third way between the Basque nationalists and the right-of-centre Popular Party, which opposes changes to the constitution.
It was not clear how much Zapatero would be able to give way to the region which already enjoys some freedoms, with its own police force and education policies.
El Pais said negotiations over a new deal would likely start after regional elections in the Basque country that should take place by May.
No one at the prime minister's office was available to comment on Tuesday but the spokesman for the Socialist party in the Basque parliament said late on Monday an end to the so-called Ibarretxe plan was not an end to dialogue.
"We hope that sooner rather than later we can start a phase of dialogue and agreement-seeking which will allow us to reach a legal framework shared by all," Rodolfo Ares said.
Two bombs in recent weeks have
dampened hopes of a ceasefire
The mainstream Socialist party and right-of-centre Popular Party say Ibarretxe's plan violates Spain's 1978 constitution, which only allows regions a degree of autonomy from Madrid.
They also say the plan divides the Basque country and favours violent Basque separatist group ETA.
In recent months there have been rumours of an ETA truce, but two bombs in the last two weeks, the latest on Sunday, have dampened hopes the group, which has killed some 850 people since 1968, will cease violence - Madrid's condition for talks.
Ibarretxe says his plan, which has been approved by the Basque regional parliament, would put an end to ETA violence. He has threatened to press ahead with a referendum even if the plan is rejected in parliament. Polls show he could just win it.
Opposition parties in Madrid have made political hay out of the fact that the plan was pushed through with the help of votes from Batasuna, a party banned as the political wing of ETA.
Batasuna had previously rejected the plan as too moderate.