The interview was published as Mr Schulz denied reports that his party was ready to enter negotiations of forming a new coalition on Friday, and accused Mrs Merkel's Christian Democrats (CDU) of leaking false information to the media.
Merkel is casting around for a coalition partner after her center-right bloc shed support to the far right in a September 24 election and her attempts to form a three-way tie-up with the pro-business Free Democrats (FDP) and the Greens failed.
Merkel would have few problems getting her parliamentary group to go along with talks about extending their current collaboration with the Social Democrats, as there is broad consensus among conservatives that a grand coalition is the only way forward. By contrast, Steinmeier - himself a former SPD leader - is known to favor the grand coalition option.
Merkel's expressed skepticism about the latter two possibilities, and following an appeal from President Frank-Walter Steinmeier, Schulz agreed to meet with the chancellor and CSU leader Horst Seehofer on Thursday night to talk about the various possibilities.
"We are under no time pressure", Schulz said, adding that there was "wide support" within the SPD leadership not to rule any course of action out.
After Merkel's negotiations to form a coalition with two smaller parties broke down, however, that left only a return to the grand coalition, a minority government, or new elections as her options.
In particular, he said he would demand German support for Emmanuel Macron's proposals for a Brussels-based finance minister and single budget for the Eurozone.
He denied a report from Germany's top-selling Bild newspaper that the SPD had already given the green-light to negotiating a new coalition with Merkel, saying "there is no automatic OK for a grand coalition, I made that clear yesterday".
Schulz also said he wants changes in Germany's approach to the European Union.
"Another senior member of Merkel's Christian Democrat Union (CDU), Mike Mohring, said he was hopeful for an eventual grand coalition and expected a new government to be formed by March".