The towering 25-year-old, who was reportedly being chased by Arsenal, Liverpool and Spurs, has been offered to the Spanish treble winners.
French newspaper L'Equipe claim Abdennour's agent Abdelkader Jilan flew to the Spanish city to discuss a possible move to the Catalan giants despite their current transfer embargo.
Barcelona have already signed Arda Turan this summer and the report claims they are prepared to buy the Tunisia international and will allow him to stay at Monaco until January 2016 when the ban ends.
Atletico have been heavily involved in the transfer market with Jackson Martinez and Luciano Vietto joining the club to replace Mario Mandzukic and Turan.
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