Both the ABC and Fairfax say Melissa Price told Anote Tong - a nominee for the Nobel Prize - that she had her chequebook ready when they met at a Canberra restaurant on Tuesday.
Mr Tong was in Australia to discuss climate change, and was dining with a Labor senator and other human rights and environment advocates when he was introduced to Ms Price.
"For the Pacific, it is always about the cash. I have my chequebook here. How much do you want?" Ms Price is reported as saying.
A spokesperson for Ms Price said the account was completely untrue.
If true, though, it would not be the first time a member of the Australian government has offended Pacific leaders in the past few years.
Former Home Affairs minister Peter Dutton was recorded in 2015 joking about rising sea levels in the region.