The PM was speaking to Canberra's press gallery last night at Parliament House's Mid-Winter Ball.
In his tongue-in-cheek address, Turnbull also poked fun at his own poor ratings in national opinion polls, drawing a comparison to Trump, whose historically dire approval ratings have dogged the first months of his administration.
"Donald and I, we are winning and winning in the polls". Not the fake polls, not the fake polls, not the fake polls! Not the fake polls!
We are winning so much.
"We are winning... not in the fake polls".
"You know the online polls. they are so easy to win". They are so easy to win. I know that, did you know that?
To more laughter, he then added: "I have this Russian guy. Believe me, it's true".
Warriors secure spot among legends by dumping Cavaliers
The Warriors won in 2014-15 but were beaten in last year's deciding series by the LeBron James-inspired Cavaliers. James had 41 points, 13 rebounds and eight assists .
"(It was) light-hearted, affectionately light-hearted", he said.
He said: "It's a breach of protocol, it's a breach of faith and all those things, but it's light-hearted, affectionate, good natured. It was fun, we've got to lighten up".
The veteran political journalist who reported the speech, Laurie Oakes, said he did not attend the ball and did not accept reporting should be banned at a function hosted by journalists.
Trump and Turnbull met briefly in NY in May on the deck of a United States aircraft carrier, where the U.S. leader said their relationship was "fantastic".
The Australian Prime Minister was reportedly kept waiting around three hours ahead of the meeting.
Malcolm Turnbull's next phone call with Donald Trump could be awkward.
In that phone call, the two spoke about a refugee swap deal between the two countries secured by the administration of former United States president Barack Obama. "That was an exaggeration", he said.
No word yet on if this means we are going to with America yet - but knowing Trump's ego, I wouldn't be surprised if the U.S. defence forces based in Darwin start pulling out the big guns... We had a great call.
He also said the refugee deal had "all worked out".
- Gunman targets Republican lawmakers, wounds 5
- Golden Years Ahead For The Golden State Warriors
- AG Sessions denies colluding with Russian Federation to aid Trump
- Warriors are National Basketball Association champions in almost ideal run through playoffs
- Rodman gives North Korean official Trump book
- House Majority Whip Steve Scalise, aides shot at baseball practice in Virginia
- Premier League fixtures: Brighton start against Manchester City, holders Chelsea host Burnley
- Russia collusion claim 'detestable lie': US Attorney General
- Cavaliers return to Cleveland after NBA Finals
- Takeaways from Cavaliers vs. Warriors NBA Finals Game 5