The Spaniards have tracked the 25-year-old since last year, but the Parisians were unwilling to sanction a move at the time.
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After another season largely spent in a supporting role at the Parc des Princes, Lee is keen for more regular playing time, making a departure increasingly likely.
PSG are already exploring potential replacements, with AS Monaco's Maghnes Akliouche among the names under consideration.
Atletico Madrid are reportedly prepared to offer around €25 million for the former Mallorca playmaker.
However, Juventus have now emerged as serious contenders. The Serie A giants are exploring alternative attacking options after encountering difficulties in their pursuit of Real Madrid midfielder Brahim Diaz.