Following their election success in two state elections late last month, the party gained another seven points to reach 28 percent voter approval, the poll for news magazine Stern and broadcaster RTL reported.
The poll result is the best ever registered for the party.
The centre-left Social Democrats (SPD) dropped two points to win 23 percent voter approval – giving the two opposition parties combined support of 51 percent, an absolute majority that would allow them to create a coalition government.
Meanwhile Chancellor Angela Merkel's ruling conservative Christian Democrats (CDU) and her junior coalition party, the embattled Free Democrats (FDP), continued to lose ground after being trounced in the recent state elections.
The CDU lost three points to reach 30 percent, while the embattled FDP lost two points to register just three percent of approval – too little to clear the five-percent hurdle for representation in the Bundestag.
With their combined approval of 33 percent, Merkel's centre-right coalition lags behind a theoretical Greens-SPD coalition by a stunning 18 points, the poll said.
The hard-line socialist Left party gained one point, but still remained in the single digits with nine percent approval.
Some 2,505 representative voters were questioned between March 28 and April 1 for by pollster Forsa.