Steinmeier, consistently among Germany's most popular politicians, has trailed Merkel in popularity, a Christian Democrat, Deutche Welle reported Monday.
Since 2005, he has served in Merkel's government.
As foreign minister, he has been in the spotlight for helping to free German hostages in Iraq and negotiating with Iran over its nuclear program, the newspaper reported.
Steinmeier, 52, was born in the western German town of Detmold. He joined the SPD in 1976.