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.