Senior members of Scholz's Social Democrats (SPD) joined the chorus of voices calling for him to make way for Pistorius, while a survey showed his popularity with the public had sunk to new depths.
Germany is set to hold elections seven months earlier than scheduled after the collapse of Scholz's three-party coalition earlier this month.
Scholz has signalled that he wants to run for a second term as chancellor, but with his party lagging in the polls, dissenters are calling for him to reconsider.
Norbert Walter-Borjans, a former leader of the SPD, said he believed Pistorius would have a better chance of beating conservative chancellor candidate Friedrich Merz, currently leading the race.
"Scholz has saved our country from many threats in an extremely difficult time," Walter-Borjans told the Rheinische Post newspaper.
"But... Merz can only be stopped with a chancellor (candidate) who has the strength to make the difference in a self-critical and approachable manner," he added.
"That has been Scholz's weak point so far," he said.
Pistorius claimed the top spot in a ranking of Germany's most popular politicians published by the Bild daily on Tuesday, while Scholz had fallen from 19th to 20th place.
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According to Bild, the SPD's top brass is planning a meeting on Tuesday evening to discuss the matter - while Scholz is on a plane returning from the G20 summit in Rio de Janeiro.
Der Spiegel magazine meanwhile reported that two influential members of the SPD in North Rhine-Westphalia, Germany's most populous state, had also come out in support of Pistorius.
"Scholz's current reputation is strongly linked to the (collapsed) coalition," SPD politicians Wiebke Esdar and Dirk Wiese said, adding that they were seeing "a lot of support for Pistorius" in their constituencies.
The embattled chancellor is also facing a backlash over his controversial decision to hold a phone call with Russian President Vladimir Putin last week.
Pistorius on Monday evening suggested he was open to running for chancellor, insisting that "in politics, you should never rule anything out".
"The only thing I can definitely rule out is becoming pope," he told journalists in Bavaria.
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