The Blur singer has recalled a conversation he had with the politician - which took place "before he became prime minister" in 1997 - and it left him "terrified".
He told the Metro newspaper's Guilty Pleasures column: "Politics is such a murky business. I would be lying if I said I hadn't considered it when I was younger.
"I even went and had a strategic meeting with Tony Blair before he became prime minister, but that terrified me so much.
"[I thought] 'I don't know if this is for me at all. I'm not a politician, I am a musician.' "
The 'Song 2' hitmaker admitted he has "strong views" and while he sees music as "escapism" rather than an outlet for his own politics, he also thinks it's the "perfect place for it".
He explained: "I have strong views. Music is escapism. It's not really there for the unpleasant truths of life.
"But I've always felt, 'No, that's the perfect place for it'. It can catch people unaware emotionally in a way nothing else can."
The 53-year-old star explained how his solo career is inspired by his concerns about politics, the environment and society as a whole.
On his new album 'The Nearer The Fountain, More Pure The Streams Flows', he took inspiration from the name of Britain's nuclear attack defences for his song 'Polaris'.
He added: "A big anxiety of my adolescence was nuclear destruction. It has now become third or fourth on the list of imminent doom and Armageddon."
Damon has found himself concerned with climate change, and said: "Solar and wind and hydro are the only thing that is sustainable. Imagine in a country as small as Britain having 15 or 16 nuclear power plants. It's terrifying."
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