The cyclist, who was stripped of his seven Tour de France titles and given a lifetime ban from the sport due to years of doping, was cleared of cancer in 1997 following a year of treatment.
Two years later, Stubbs was diagnosed, resulting in the removal of his testicle, and had another operation 18 months later when a tumour appeared near to his spine.
"I read Lance Armstrong's book and it inspired me," Stubbs told the Daily Mail.
"I know what happened to him as a sportsman turned out to be very different but he still went through a horrible illness.
"He was a cheat as a sportsman but he could not cheat his illness. I respect him for fighting it, even though I don't respect him as a sportsman. I think you have got to separate the two."
Stubbs now works as part of the coaching staff at Everton.