The Italy midfielder has emerged as among the best players in the world.
Di Biagio told TVPlay: "Barella is one of those I raised, he was 18 years old when he was with me in the Under 21s and they called from City for information.
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"What was he like? Today it's easy to say, at that moment I said 'get him immediately'. When a team asks you how he is as a person it means that on a technical level they know him.
"So I took the liberty of telling them to get him immediately because he has incredible margins for improvement.
"Then he took another path, better for Inter."