Backing from Schaeuble, the former finance minister who drove Europe's fiscally austere response to southern Europe's debt crisis after 2008, would give a stiff tailwind to businessman Friedrich Merz's candidacy.
The next party leader will be in pole position to succeed Merkel as chancellor of Europe's economic powerhouse, though Merkel has said she wants to remain in post for three more years after quitting the CDU leadership.
Victory for Merz in next month's party leadership election would signal a shift towards the low-tax, business-friendly right-wing conservatism that Merkel has pushed into the background during her 13 years as chancellor.
Schaeuble, like Merz, once was tipped as a future leader and chancellor before Merkel outmanoeuvred first one then the other.
Surveys suggest that Merz - who holds numerous non-executive company board positions, including chairman of the German arm of the U.S. asset manager BlackRock, enjoys more public support than CDU general secretary Annegret Kramp-Karrenbauer, seen as the heir to Merkel's centrist course.
A survey by pollster Civey for newspaper Die Welt found that 49 percent of voters believe that of the three candidates seeking the CDU chair, Merz is the most capable of improving the party's election results.
The survey showed that 19 percent of the 5,045 voters polled on Thursday and Friday believed Kramp-Karrenbauer would be best at boosting the CDU, with just 6 percent backing the third candidate, Health Minister Jens Spahn.
According to Der Spiegel, Schaeuble urged Merz to throw his hat into the ring after Merkel announced her withdrawal following setbacks in two regional elections.
Merz has coined the idea of a German 'Leitkultur', or 'lead culture', with which he called on Muslim immigrants to assimilate and to adopt German values and traditions.
He served in the German parliament from 1994 to 2009, including two years as parliamentary leader of the conservative bloc. He also is known for a proposal to simplify the annual tax return so that it could be written on a beer mat.
No response to the Spiegel report was immediately available from the parliamentary press office.
(Reporting by Thomas Escritt Editing by Kevin Liffey and Raissa Kasolowsky)
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)