Treasurer Josh Frydenberg is being targeted by a new campaign to drive him from Parliament in a powerful bid by the Greens, who are running veteran barrister Julian Burnside QC as their candidate for Kooyong at the May election.

Mr Burnside will announce his campaign on Tuesday in a move that throws open the contest for the prize Liberal electorate, escalating the threat to Mr Frydenberg in a seat the Morrison government cannot afford to lose.

Julian Burnside will run as the Greens candidate in the seat of Kooyong against Treasurer Josh Frydenberg. Credit:Jason South

A longstanding advocate for human rights and asylum seekers, Mr Burnside is going back on his previous vow to stay out of politics after decades of involvement in the law.

"I've always said I wouldn't go into politics. 'Don't wrestle with a pig,' the saying goes, 'because you both get covered in mud and the pig loves it'," he writes in an explanation for his decision.