Spanish publication Fichajes suggests that Digne, 23, rejected advances from the Anfield club who were desperate to sign a new left-sided defender during the summer transfer market.
However, the France international opted for Camp Nou with Barca paying an initial fee of close to £14million.
Digne made his Barcelona debut in the Spanish Super Cup against Sevilla earlier this month as a first-half substitute and has since notched three appearances, including a La Liga debut as a second-half sub against Athletic Bilbao last week.
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