Forty percent of Germans hope Steinmeier, currently in his second term as foreign minister, will be the country’s next leader, the Forsa poll for Cicero magazine found.
In recent months, he has taken a prominent role in European efforts to mediate in the conflict in Ukraine.
When Steinmeier led his centre-left Social Democratic Party (SPD) into the 2009 election, the party won only 23 percent of the votes. It was its worst performance in six decades. But in February, he overtook Merkel in an opinion poll, ousting her from the top spot as Germany's most popular politician for the first time in two years.
The second choice in Thursday's poll was Defence Minister Ursula von der Leyen, a member of Merkel's centre-right Christian Democratic Union (CDU). She has been frequently topped to succeed Merkel and 15 percent of respondents said they wanted to see her as Merkel's successor.
SPD leader Sigmar Gabriel, who serves as economy minister and vice-chancellor in Merkel's cabinet, received 14 percent in the poll. And one in ten voters supported interior minister Thomas de Maizière (CDU).
Von der Leyen is seen as the most likely CDU candidate to succeed Merkel should the chancellor step down before the next general election, scheduled for 2017.
German media reported this week that Annegret Kramp-Karrenbauer (CDU), the state premier of Saarland, was Merkel's preferred successor.
Merkel has not said whether she plans to leave office before the next election.
The poll was conducted among 1,008 adults in June.