China's ambassador to Australia Xiao Qian said he had been working with the foreign affairs department on a high-level meeting between the leaders, potentially on the sidelines of the G20 summit in Indonesia in November.
Mr Albanese said he would look forward to such discussions should they take place.
"I'm open to dialogue with anyone at any time, particularly with leaders of other nations," he told reporters in Canberra on Wednesday.
"It's a good thing if there is dialogue, and certainly, if such a meeting took place I would welcome it as I welcome dialogue with leaders throughout the region and throughout the globe."
However, Mr Xiao said action was needed from both countries in order to improve the relationship.
"It needs action to be taken from both sides to improve the relationship. There's no autopilot mode," he told the ABC's 7.30 program.
"As to exactly where exactly halfway between us, we can talk about those, but we need efforts from both sides."
The ambassador said it was important that nations like China and Australia maintained top level dialogue, revealing he has been trying to seek common ground with the Department of Foreign Affairs and Trade.
"A top level meeting is not a meeting for a meeting's sake, we're expecting a meeting to be constructive instead of destructive."
Mr Xiao said he was aiming to get imprisoned Australian journalist Cheng Lei access to her family.
Ms Lei, who has been detained in China for more than two years accused of "supplying state secrets overseas", hasn't been able to speak to her children since her arrest.
Mr Albanese said the journalist must be able to see her children.
"This is something that should happen. Cheng Lei should have access to her family," he said.
"Australia continues to make representation and we have a very strong view about her treatment, and we'll continue to make representation.
"There's been no transparency in any of these processes at all, and the Chinese government needs to do better."
Opposition foreign affairs spokesman Simon Birmingham said he welcomed the Chinese ambassador's words around family access for Ms Lei.
"I do urge China still to make transparent arrangements in relation to this case, to give some certainty in relation to the charges for sentencing," he told ABC radio.
"But I do welcome the fact that Chinese ambassador indicated that he has been making representations for her to have access to her children."
The Australia-China relationship remains heavily strained.
Earlier this week, Foreign Minister Penny Wong described a United Nations report into China's mass detention of the Uighurs as "harrowing reading".
The Chinese ambassador hit back, labelling the report an "absolute fabrication".
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