Flick met with Barca sports chief Deco in London to discuss a deal. If Xavi departs, the German will be appointed his successor.
El Chiringuito says Barcelona have reached an agreement with the 59-year-old.
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Flick, who was most recently Germany coach, has agreed a two-year contract.
He started learning Spanish in January when Xavi announced that he would resign - before the Barca coach reversed his decision.
Flick also hired Pini Zahavi last winter to boost his chances. The agent has a very good relationship with Barca president Joan Laporta and represents Robert Lewandowski.