An opinion poll places the Social Democratic Party (SPD) within a point of Merkel’s Christian Democratic party.
The poll also predicted a clear victory for Mr Schulz in a direct vote against the beleaguered Chancellor.
Support for the SPD has been boosted by the appointment of Mr Schulz as their nominee for the leadership after the former European Parliament president left his powerful role in the EU to take on Merkel.
t comes after President Trump accused the EU of being a 'vehicle for Germany'
Before returning to mainstream German politics, Mr Schulz had spent decades working within the EU.
For the past four years the CDU and SPD have been ruling together in a grand coalition after results in the 2013 election shut out the CDU's preferred coalition partner, the Free Democrats (FDP).
The far right Alternative for Germany (AfD) are also set to gain from Mrs Merkel’s unpopularity and become the third biggest force in the central European superpower’s lower house.
Their public support was buoyed by opposition to Merkel’s controversial open door immigration policy amid the height of the immigration crisis.
'MERKEL MUST GO': Brussels protest against German Chancellor Thu, January 12, 2017
Angry campaigners held placards with slogans reading 'Merkel not welcomed' and 'Merkel must go' following a spate of terror attacks against Germany.
Play slideshow EPA 1 of 11
Protest on the sidelines of Angela Merkel's official visit in Brussels
The poll found Mr Schulz would win the leadership if the election was held today
It comes after President Trump accused the EU of being a “vehicle for Germany” to wield power over the rest of Europe.
Get Quotes on Home Insurance
His comments came as he praised the British people’s decision to leave the crumbling bloc and predicted many more countries would follow their example.
He said: “I believe others will leave.
For the past four years the CDU and SPD have been ruling together
Mr Trump's comments came as he praised the British people’s decision to leave the crumbling bloc
“I do think keeping it together is not going to be as easy as a lot of people think.
“And I think this, if refugees keep pouring into different parts of Europe it’s going to be very hard to keep it together because people are angry about it.
“You look at the European Union and it’s Germany. Basically a vehicle for Germany.
“That’s why I thought the UK was so smart in getting out.”
- Arron Banks condemns Chancellor Mekrel over Berlin attack
- Merkel critic QUITS party, claims CDU support illegal immigration
- German soldiers deployed in Lithuania over Russian invasion fears