Laporta is seeking a replacement for Xavi, who will step down as Barca coach at the end of the season.
Foot Mercato says in recent days there has been a meeting between Laporta and Flick, along with the former Bayern Munich coach's agent.
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Bara's board is attracted by the winning record of Flick (two Bundesliga titles).
The interviews will continue, but at the moment Flick seems to be in pole position.