Terry played with some of the Premier League's all-time greats during his time at Stamford Bridge but Wollaston is likely unknown to many fans.
The midfielder had a chance to break into the first team under Ruud Gullit in the late 1990's but Terry explained he struggled to bridge the gap between the academy and first team.
When asked about players who never fulfilled their potential at The Blues, Terry replied: "Probably a boy called Rob Woollaston at Chelsea.
"He was like a midfielder/winger, had so much ability.
"I still know Rob now, but mentally didn't have that to go and push himself."
The 39-year-old goes on to explain the key incident which made him realise Wollaston may not make it at Stamford Bridge.
"He got chose to train with the first team at a really young age, 17 or 18, did really well and Gullit told him he was going to play in the first team in a cup game.
"He then phoned up on the day of the game and said he was sick.
"All of us, if we were sick or felt like we were at the end of the world, we would have still gone and played the game, we wouldn't have given up that opportunity.
"He actually done it two or three times and he was just not mentally ready for the game, but ability-wise, incredible."
Terry spent 19 years at Chelsea and won a slew of trophies but it could have turned out differently.
He also revealed in the Instagram Live that only two clubs ever attempted to lure him away from London - Huddersfield Town and Manchester City.
"During my time the only two clubs that approached me were Huddersfield when I first came through. Steve Bruce was manager of Huddersfield," Terry recalled.
"Chelsea accepted a bid and [Gianluca] Vialli said no. Which obviously I'm very thankful to Luca for, he gave me my debut."
City made a bid for him in 2009 but it's a move Terry wasn't keen on.
"Man City approached Chelsea, made an offer official.
"I sat with the owner, face-to-face and said 'I never want to leave Chelsea, that's a fact. If you want to sell me then it's a different story, I clearly don't want to stay. But I'm telling you off the bat that I never want to leave this football club'.
"Within that, I was due a new contract, we shook hands on a new contract, agreed a deal and I stayed another five, six years after that."
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