If Germans could choose the chancellor directly, Steinmeier would get just 27 percent of the vote versus 60 percent for Merkel, according to the survey commissioned by public broadcaster ARD.
Though Germans vote for political parties and not individual candidates to lead the country, the so-called “chancellor question” is seen as an important barometer of public sentiment.
Merkel managed to improve her poll rating among likely voters by five points from last month's survey, while Steinmeier lost five points.
The news that Germans don't see the current foreign minister as cut out for the Chancellery is the latest piece of bad news for Steinmeier and his centre-left Social Democrats.
The party took a beating in Sunday's European Parliament elections, drawing a record low 20.8 percent of the vote against the 37.9 percent share that Merkel's conservative Christian Democrats (CDU) and their Bavarian allies, the Christian Social Union, drew.
Looking forward to the September 27 elections, the poll showed the CDU/CSU union garnering 36 percent support from likely voters, a two point increase from the last survey. Support for their possible coalition partners, the free-market Free Democratic Party (FDP), was unchanged at 14 percent, meaning the conservatives and FDP could form a majority government.
The SDP got support from 25 percent of voters, a two point drop from the previous poll.
Though Steinmeier fares dismally as a candidate for chancellor, Germans are happy with the job he's doing as foreign minister: 63 percent of the survey respondents said they were pleased with his work as Germany's top diplomat.
The ARD telephone survey was carried out by the polling firm Infratest dimap from Monday to Wednesday of this week with 1,500 voting-eligible participants from across Germany.