The survey for RTL television and Stern magazine suggested 74% of Germans were in favour of allowing homosexuals to marry and 23% against.
Support is strongest among people voting for the opposition Greens and centre-left Social Democrats (SPD) but even among those backing Merkel’s Christian Democrats (CDU), almost two-thirds were in favour, the poll showed.
The CDU wants to boost its appeal among urban voters as it gears up for this year’s vote.
Merkel’s government is preparing to amend the law to grant same-sex couples greater adoption rights after Germany’s constitutional court ruled last week that gay people should be allowed to adopt a child already adopted by their partner. Heterosexual couples already have the right.
The court has given the government until July 2014 to amend the law.
Last weekend, a close Merkel ally hinted that the party may also be ready to abandon its opposition to giving gay couples the same preferential tax treatment as married heterosexuals.
Homosexuals in Germany can form civil partnerships but cannot marry. Opposition parties accuse the CDU, staunch advocates of traditional family values, of dragging their feet on gay rights.
The CDU’s more conservative Bavaria-based sister party, the Christian Social Union (CSU), has warned against rushing to change the law.
Earlier this month, the lower houses of parliament in both France and Britain voted in favour of gay marriage.