Before last night's Champions League defeat for his PSG by Barca, Enrique claimed his style of play suited the Blaugrana better than the work of Xavi.
But Koeman, who like Enrique coached and captained Barca, says only three men can lay claim of such standing.
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He told Cataluyna Radio: "Bara DNA? There are only three people who represent Bara's DNA: Johan Cruyff, Pep Guardiola and Lionel Messi.
"I saw the pictures yesterday of Luis Enrique and Xavi before the match and they looked like very good friends. But the day before I see Luis Enrique make some bizarre statements. I think there is more than we can see between these two coaches."