SYDNEY, Apr. 11 (Reuters) - China's Premier Li Qiang will visit Australia in June, the South China Morning Post said on Thursday, the latest step in a thawing of ties between the two nations.

Australia and China, its largest trading partner, are rebuilding ties after a period of strained relations, which hit a low in 2020 after Canberra called for an independent investigation into the origin of COVID-19.

The visit in the third week of June will coincide with a lifting of an unofficial three-year ban on Australian live lobsters, the paper said, citing two sources with knowledge of the matter.

A spokesperson for Australia's department of the prime minister and cabinet declined to comment.

A spokesperson for China's foreign ministry said she had no specific information on the visit when queried at a regular press briefing.

"We are ready to stand with Australia ... to strengthen high level exhanges, deepen co-operation, increase mutual understanding, and bring China-Australia relations onto a more mature, stable and fruitful track," said the official, Mao Ning.

Since a change of government in Canberra two years ago, Beijing has agreed to lift most of the tariffs on Australian goods, including barley and wine, with lobsters one of the last commodities facing curbs.

"We welcome the efforts ... to improve diplomatic relations," said a spokesperson for Geraldton Fishermen's Co-Operative, Australia's largest rock lobster exporter.

"Restoring market access is a win-win and will contribute to Australia's economy through export earnings, jobs and regional development."

Following a visit by Chinese counterpart Wang Yi, Foreign Minister Penny Wong said last month that she was expecting a visit from Li this year, without saying when.