Anthony Albanese met with EU chief Ursula von der Leyen on the sidelines of the G20 summit in Johannesburg after earlier indicating negotiations on the agreement could be finalised by early 2026.
Scrapping Australia's luxury car tax - a bugbear of European exporters - could be on the cards to secure the deal after Mr Albanese said he did not want to rule anything out from the discussions.
"What I'd like to see is (a trade deal) finalised in the first quarter of 2026," he told reporters in South Africa.
"This would be very important."
Trade Minister Don Farrell said his talks in Melbourne with his European counterpart were also positive, adding there was renewed optimism on a deal being struck after years of failed negotiations.
US President Donald Trump and Chinese President Xi Jinping both opted to skip the annual leaders' meeting, leading to suggestions the forum would be a damp squib.
However, Mr Albanese defended the value of multilateral meetings such as the G20 and Quad despite Mr Trump's isolationist stance.
"My job is to represent Australia's interests and we continue to participate constructively," he said.
"We engage in bilateral forums, but you need multilateral forums as well where you get that engagement across the board - and that is why the G20 is so important."
Mr Albanese has a busy three-day schedule, which includes meetings with Indian Prime Minister Narendra Modi, South Korean President Lee Jae-myung and Turkish President Recep Tayyip Erdogan.
The bilateral with the Turkish leader comes after Australia relinquished its bid to host the United Nations' annual climate summit to Turkey following drawn-out talks and negotiations.
La Trobe University international relations professor Bec Strating said the G20 followed an effective year abroad for the prime minister, with the end of summit season providing an opportunity to bolster relations.
"Australia has been really taking the lead on issues of conflict prevention in the region, so it's been quite a solid year already for Australia in terms of foreign policy," she told AAP.
Prof Strating cited success in landing a critical minerals deal with the US, a security pact with Indonesia and partnerships in the Pacific as evidence the approach of quiet diplomacy was working in advancing Australia's agenda overseas.
"Developing these partnerships and really investing in relationships across the region, I think, is paying off dividends," she said.
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