He added: "I get concerned. I do recognize that it probably affects you in short-term memory more than long-term. I know with me, I have days I can't find words. I literally cannot find words or the name of somebody I know. That gets a little scary. Those days happen when I'm tired."
Simpson only suffered two concussions in his career at the Buffalo Bills and San Francisco 49ers before he was embroiled in a legal saga over the 1994 murders of his ex-wife and her friend, ultimately acquitted then jailed for armed robbery in 2008.
That is the same number of concussions as Aaron Hernandez, the disgraced Patriots tight end who was last year diagnosed with one of the worst cases of CTE ever seen in an autopsy after he committed suicide at the age of 27 while in jail for murder.
If he does have CTE, it wouldn't surprise the nation's top CTE researchers, who insist that repeated head hits are the real risk factor, and concussions are a 'red herring' that the NFL is trying to focus on because it is a 'manageable' problem.
His words come days after Mark Gastineau, the 61-year-old former New York Jets star, wept live on air talking to radio host Pete McCarthy as he said football had ruined his life by leaving him with dementia, Alzheimer's and Parkinson's.
And last month, Emily Kelly, wife of 43-year-old former New Orleans Saints player Rob Kelly, wrote a harrowing account in the New York Times about her husband's aggression, paranoia and suicidal thoughts just a few years after he was forced to retire due to injury.
Scores of late players have been diagnosed with CTE posthumously - many after committing suicide - including Aaron Hernandez, Junior Seau, and Dave Duerson.
More than 1,800 former NFL players, boxers, and military veterans have pledged to donate their brains to the Concussion Legacy Foundation for CTE research.
Boston University has made huge headway in investigating chronic traumatic encephalopathy (or, CTE), the Alzheimer's-like disease which has been linked to repeated blows to the head from contact sports.
Researchers are still unclear on how CTE affects behavior, but a growing swell of studies is offering some answers.
CTE sufferers have clumps of tau protein built up in the frontal lobe, which controls emotional expression and judgment (similar to dementia).
This interrupts normal functioning and blood flow in the brain, disrupting and killing nerve cells
By stage 3 - i.e. Aaron Hernandez's stage - the tau deposits expand from the frontal lobe (at the top) to the temporal lobe (on the sides). This affects the amygdala and the hippocampus, which controls emotion and memory.
This year, the team has published a slew of research papers showing links between football and brain injury.
While there is still no way to diagnose the disease during life, the evidence bridging the gap between head hits and neurodegenerative diseases is strengthening at an unprecedented rate.
"I don't know of any other area of scientific investigation that has had such a large and pure impact on awareness in lay culture and attention within the scientific community," Dr Robert Stern, head of Boston's CTE research unit, told Daily Mail Online this week.
"This has been a landmark year for media coverage and cultural awareness of CTE and long-term consequences of playing football.
"We still have a tremendous amount of work ahead of us to be able to answer some very important questions about CTE, but we should have a test to diagnose in life within the next five to 10 years - and that's being conservative."
One of Boston University's papers published in 2017 found those who start playing football from before the age of 12 - as most professional players do - have a much higher risk of mood, behavioral and neurological problems in later life compared to those who start later. They attributed this to the damage of repeated hits to the head at such a critical time of brain development.
Another showed 110 of the 111 former players brains they had in their lab, donated from families after death, had signs of CTE, showing that it's not a trivial number of people that get the crippling disease.
Perhaps most importantly, last month Boston published a groundbreaking study to demolish the obsession with concussions.
Concussions, they found, are the red herring: it is not a 'big hit' in football that causes CTE or makes it more likely. Rather, it is the experience of repeated subconcussive hits over time that increases the likelihood of brain disease. In a nutshell: any tackle in an NFL game - or even practice - increases the risk of a player transforming into the 'ghost' of a human, according to Dr Stern.
