The offer - from a friend of a former AFL fitness coach - was in 2005, shortly after he suffered a serious leg injury when playing with the Tigers.
"It was a human growth hormone that would have had to have been injected," he told Melbourne's Triple M.
Brown admitted he thought about accepting the offer.
"I did think about it for a fleeting moment but I just thought about how often you'd be looking over your shoulder if you actually went through with it and I don't think I could have lived with that guilt."
Brown said he researched the effects of human growth hormone following the offer, and often thought about it as he battled to regain fitness.
The claim comes on a dark day for Australian sport following the release of an Australian Crime Commission report detailing the widespread use of banned substances, as well as links to organised crime, across major sports throughout the nation.
Brown is the second former AFL player to admit to being offered performance enhancing drugs since the Essendon supplement scandal broke on Tuesday.
On Wednesday, former Port Adelaide captain Warren Tredrea revealed he was offered banned substances during his career.
