The 66-year-old former all-rounder, who played for England between 1972 and 1977 before becoming a commentator, will undergo a biopsy to know at what stage the disease is and what needs to be done for its cure.
"I have had a few scrapes in my life and this is another one. Vivian (Tony's wife) and I are going to put the boxing gloves on and fight this like we've never fought anything before," Greig is quoted as saying by 'Sunday Telegraph'.
Greig, who was initially diagnosed with bronchitis in May, has a lesion on his right lung.
After returning to Australia from the ICC World Twenty20 in Sri Lanka, he had "a lot of fluid" drained from the lung, and further testing revealed he had cancer.
Greig said he is yet to ascertain if will be working over with Channel Nine as commentator during the Australian summer.
"At this stage, the summer is totally up in the air. My priority, 100%, is my family. They will come first," he said.
Greig played 58 Tests for England and scored 3599 runs for an average of 40.43 apart from taking 141 wickets.
Of the 22 One-day internationals that he played, he could score 269 runs for an average 16.81 and claimed 19 wickets.
