Mr Albanese confirmed he has received a letter from the Chinese premier and would respond in due course upon returning to Australia following Tuesday's Quad meeting in Tokyo.
Australia would seek to work with all countries but would not compromise on its values, Mr Albanese said.
"It's not Australia that's changed, it's China," he told reporters following the leaders' summit.
"It's China that has placed sanctions on Australia. There is no justification for doing that and that's why they should be removed."
The incoming Labor government will seek to build relationships across the Pacific and Asia in a renewed focus on the region.
"We want peace and stability in the region," the prime minister said.
"That's best achieved through proper diplomatic processes by making sure we build relations in the region and act in a positive way."
But Mr Albanese also reiterated that a list of 14 demands by the Chinese government to repatch the bilateral relationship, which was subsequently leaked to the Australian media, was "entirely inappropriate".
"We reject all of them," he said.
The remarks came after China's premier reportedly said Beijing is willing to push forward bilateral ties with Canberra.
"The sound and stable development of the Sino-Australian relationship conforms to the fundamental interests and common aspirations of the two peoples and is also conducive to peace, stability, development and prosperity in the Asia-Pacific region," the China Daily reported Mr Li as saying.
Mr Li said this year marked the 50th anniversary of the establishment of Sino-Australian diplomatic ties, noting the Labor Party made the right decision in the 1970s to establish a relationship with China.
Australia's relationship with the regional powerhouse has soured in recent years, with Beijing refusing to take calls from the outgoing Morrison government and blocking imports on a variety of goods despite a free-trade agreement between the two countries.
China is still Australia's biggest trading partner, especially through the shipments of iron ore.
Asked whether China was now out of the "deep freeze", Treasurer Jim Chalmers told ABC radio on Tuesday: "We want to work with countries in our region to make sure it is stable and prosperous".
"That's why the developments on the trade front are so exciting, because we want the region to grow strongly," Dr Chalmers said.
"We want all of our economies to benefit from that and we will engage with countries in the region on that basis."
It comes after US President Joe Biden warned Beijing not to interfere with Taiwan or the US would intervene militarily.
Mr Albanese maintained that Australia's position hadn't changed after President Biden said his remarks were in line with the established US position of strategic ambiguity.
"Our position is there should be no unilateral change to the status quo. Our position has not changed," he said.
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