Schulz, the former president of the European Parliament, vowed to extract a high price if the SPD supports Merkel for a fourth term from early 2018 at the helm of Europe's biggest economy.
He reiterated that the eurozone should have more investment and a common finance minister and budget.
The drafting process of such a constitutional treaty, Schulz said, should involve citizens across the Continent.
Martin Schulz, the leader of the Social Democratic Party, told his party conference that he wants the continental bloc to move in the direction of a US-style federal union.
Schulz said only a more united European Union could meet major challenges such as combating climate change, managing mass migration or stopping multinational companies from dodging taxes.
He also argued that only a strengthened European Union would stop the advance of right-wing nationalists, citing gains they had made in Germany as well as Austria, Denmark, Finland, France and the Netherlands.
'If we don't change course, if we don't strengthen Europe in very practical and concrete ways, then these forces will win, ' he warned.
He also refused to join a new coalition after Merkel's talks with two smaller parties collapsed last month.
Over the next few days he will attempt to embolden members with a four-page manifesto of demands the SPD would take with it into any coalition talks.
Schulz has said any decision would first have to be put to the party's rank and file in a vote, meaning that any exploratory talks could not begin before January, and any grand coalition that was agreed on would not be likely to come together before Easter.
The leader of Germany's Social Democrats (SPD) said on Thursday that the country must find a way to exit brown coal production without hurting coal-producing regions and causing job losses.
SPD members will also be asked to examine the possibilities of tolerating a minority conservative government or even opting for new elections - the least popular choice among the German public, according to polls. Any final deal will go to SPD members for a vote of approval.