Talking to Germany's Bild television on Tuesday, the chancellor-in-waiting said he would like to see mandatory vaccinations "not too far away in the future, so I suggest beginning of February or March."
At the same time, he said that the decision would be made in the parliament, and that it would be a "matter of conscience" for individual lawmakers.
Germany's Federal Medical Association also called for a vaccine mandate to put a stop to the "endless loop of lockdowns."
It urged the German government to make arrangements that would apply to "all adult citizens with no medical contra-indications against a vaccine."
The question of mandatory vaccination is considered controversial in Germany, partly due to forced medical treatments during the Nazi-era.
Separately, spokesman for the outgoing German government Steffen Seibert said a decision on the vaccine mandate would be made "soon."
Pharmacists to be allowed to give vaccines
The latest comments come after Scholz and outgoing Chancellor Angela Merkel attended a video-conference with the premiers of Germany's 16 federal states.
The country's top officials agreed to boost the vaccination campaign by administering 30 million more vaccines before Christmas, according to Seibert.
In order to achieve this, they will include new categories of people who are allowed to administer jabs. This will most likely include pharmacists. However, final conclusions from the meeting won't be published before Thursday, according to the statement.
Some 68.5% of Germany's population of roughly 83 million have been fully vaccinated.
What else is being discussed?
According to Reuters news agency, Scholz also supported the idea of introducing so-called 2G rules for customers in retail stores, meaning they must be either vaccinated ("geimpft") or have recovered ("genesen") from COVID-19. The rules would not apply in supermarkets or drugstores.
Reuters said that Scholz had pledged to make changes to the Infection Protection Act to provide "states with high infection rates with a suitable set of instruments."
Scholz also introduced Major General Carsten Breuer as the head of a planned COVID crisis team to be set up when the new coalition government commences work. The team is to primarily speed up Germany's vaccination program, including the administering of booster injections.
States governed by premiers from Scholz's Social Democrats (SPD) called for the the protection given by vaccination to be officially recognized only for six months, the daily Rheinische Post reported, citing the waning efficacy of the vaccines after that period.
The paper said the SPD premiers also wanted strict rules on the number of contacts unvaccinated people could have at a time.
Lockdowns loom large
Also on Tuesday, the Federal Constitutional Court ruled that the "emergency brake" imposed by the federal government from April to June was compatible with the constitution. Under the measure, districts and regions were required to implement curfews, contact restrictions and other curbs when the infection rate rose above certain levels.
Several state premiers have called for similar nationwide measures to be reintroduced as Germany struggles to contain a fourth wave of the pandemic that has recently been additionally complicated by the advent of the omicron variant.
tj,dj/nm (dpa, Reuters)