According to a report in Friday's edition of the Bild newspaper, Schäuble thinks the only way out of the current debt crisis in the eurozone is if the EU completely transforms its contract with member states.
He says far-reaching reforms are necessary, "even if we know how difficult a treaty change will be."
Finding an agreement that all 27 members of the EU can sign up to is a notoriously difficult undertaking.
The latest attempt to give the EU a common constitution failed some years ago when several governments could not get the agreement past referendums. The Lisbon Treaty, which was eventually ratified, was a significantly watered down version of the constitution.
Schäuble's proposal would also draw a clear line between the 17 countries that use the euro, and the other ten – including Britain – that don't.
The CDU leadership also agreed on Thursday to allow the German parliament a say in any future billion-euro bailout deals of the EU fund European Financial Stability Facility (EFSF).