"I have had a few scrapes in my life and this is another one," South African-born Greig, 66, told The Sunday Telegraph in Australia.
"Vivian (his wife) and I are going to put the boxing gloves on and fight this like we've never fought anything before."
Greig will undergo a biopsy next week on his lung to precisely diagnose the seriousness of the cancer.
Greig said that he first became aware that he had a problem when he was commentating on Australia's series against Pakistan in the United Arab Emirates in September.
On his return from the World Twenty20 in Sri Lanka, he said he had "a lot of fluid" removed from his right lung and tests revealed he had cancer.
As well as his spell as England skipper, Greig also became a leading figure in the Kerry Packer rebel World Series Cricket in 1977 which sent shockwaves through the sport.
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he is undoubtedly the greatest commentator of all time
What's going on with the cricket fraternity of late. Our prayers are for your quick recovery and health.