Reilly – who had a short spell at the club in the 1980s – is best known for scoring the winning goal for Watford in the 1984 FA Cup semi-final against Plymouth Argyle.
And the Bellshill-born player has opened up about his diagnosis in an interview with magazine Backpass.
"My short-term memory is terrible, but long-term is fine," said Reilly. "It's called Chronic Traumatic Encephalopathy, and there's research going on all the time.
"Mine seems to be at the back of the skull, not the front. I think it was more centre-halves heading me in the back of the head rather than heading balls that has caused the problem.
"It's a degenerative illness, and I need to take tables. The football authorities have brushed this under the carpet, because they've had this knowledge for some time.
"There are lots of former gridiron players and footballers who have suffered severely. Some are lonely and desperate and end up drinking themselves to death without support. I think i's tragic.
"Men never used to talk about these things, but now, in 2019, more and more players are talking, because they know by sharing they can help themselves and others.
"I'm lucky. I have the love of my family and friends and my lovely finance, who I'm going to marry this July. Without her, I don't know where I would be, drinking or gambling maybe. I couldn't cope on my own, I know.
"But, at the moment, I can get about, play some golf and have a few pints of Guinness. That's more than enough."