According to French newspaper Le Parisien, the reigning European champions remain alert to potential opportunities in the market as concerns persist over Safonov's performances.
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The Russian international established himself as PSG's No.1 midway through last season, replacing Lucas Chevalier, who had previously succeeded Gianluigi Donnarumma.
Chevalier struggled to meet expectations following his arrival from Lille, prompting another change between the posts.
PSG's interest in Japan international Zion Suzuki during the summer highlighted their desire for further competition, although the goalkeeper eventually joined Aston Villa.