Unusually, I'd like to ask what your source is for this question? I've not seen this claim made in any of the literature I'm familiar with on Spain and Germany during the Second World War. I'm hardly an expert in Basque nationalism or the Nazi regime, but I would have expected something like this to come up somewhere in the many books on the question of Franco and Hitler.

The closest I've been able to find on the subject of Nazism and Basque independence is through a man named Martín de Arrizubieta, who was a defrocked Basque priest who had fought for the Republic, but ended up in Berlin in the 1940s (potentially having been captured after a stint in the French Foreign Legion, but I've been unable to confirm that in a scholarly source). De Arrizubieta was by 1944 a committed Nazi ideologue, part of a small sect of Spanish Nazis based around the Instituto Ibero-Americano in Berlin, led by Nazi diplomat Wilhelm von Faupel, who had been the German representative in Spain during the civil war. The Institute took over the newspaper Enlace, which had previously been a pro-Franco paper aimed at Spanish workers and soldiers in Germany, after the paper ran out of money. Many of those remaining in Germany were veterans of the old Blue Division, who had refused to return to Spain when the division was recalled by Franco in 1943. By this stage, many of the more committed Nazis among them had grown hostile to Franco due to his attempts to realign himself towards the Allies and away from Germany.

Martín de Arrizubieta was made the editor of the relaunched Enlace, and came to advocate through its pages a bizarre mix of Nazism and Basque nationalism, advocating for German invasion of Spain after the Allies were defeated and the installation of a true fascist government. The Germans, de Arrizubieta insisted, should no longer 'respect the Spanish frontier.' He dreamed, evidently, of a racially pure Basque state that would be given its independence by a new National Socialist regime in Madrid. He survived the defeat of Nazi Germany, eventually returned to Spain and faced prosecution for his wartime anti-Franco activities. He apparently continued to be involved in anti-Franco groups and movements for several decades in the Basque Country and elsewhere, although I don't have any reliable sources discussing his later life.

Although Martín de Arrizubieta certainly held the ideological positions you mention, it's worth noting that he doesn't quite fit the general thrust of your question. For one, there is little indication that he was taken seriously (or even noticed) by the Nazi regime, or that they ever actually considered his proposals or had a particular interest in the Basques. For another, it wasn't until 1944 - and the whole issue was fast becoming a moot point - that he began to air these views in Berlin. In histories of Spanish-German relations during the Second World War, Martín de Arrizubieta is a footnote (quite literally in the case of Stanley Payne's Franco and Hitler: Spain, Germany, and World War II).