Mazraoui comes off contract at the end of the season and is now free to negotiate pre-contract terms with interested foreign clubs.
AC Milan and Borussia Dortmund are both interested, though now Barca have stepped forward for the fullback.
Sport says Barca have already made a first formal proposal to the player and they are leading the race for his signature.
Mazraoui's agent, Mino Raiola, met with Barca president Joan Laporta in Turin in December to discuss terms.
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