Greens leader Richard Di Natale has declared he would "relish" the chance to serve as health minister in a future Labor-Greens coalition government, and suggested colleagues such as Larissa Waters could also serve in cabinet in charge of portfolios such as environment.

The ambition, revealed in an exclusive interview with Fairfax Media to mark Senator Di Natale's impending six month anniversary as leader, came as Prime Minister Malcolm Turnbull met the Greens leader for the first time on Thursday, in a clear sign of the new Liberal Prime Minister's determination to reach out to the crossbench and advance his government's agenda.

In the interview, Senator Di Natale said his personal view was it would be a mistake to enter into a formal, permanent alliance with Labor akin to the Liberal-National Coalition but "I think we can enter into an arrangement with the Labor party to support them in government in the same way we have [in 2010] – you offer confidence and ask for key policy outcomes and you do that election by election," he said.

"We should be open to cabinet posts, we have done that already in Tasmania and the ACT. My view is you are in politics to get outcomes. I would relish the opportunity to be a health minister in a future government ... why couldn't we see [Senator] Larissa Waters as an environment minister in a future government?"