The Toulouse defender was reportedly invited to watch Barcelona's recent Champions League match against AC Milan, as the Catalan club look to bring in centre-back cover at the end of the season.
Arsenal and Manchester City have also been linked with a move for the versatile defender, but Abdennour admits he would welcome the opportunity to play for a club like Barcelona.
"I know that Barcelona are following me and four other defenders, at least" Abdennour told Radio Montecarlo.
"If there is to be an offer from them at the end of the season then I will not say no, but Toulouse's president will decide."
The Tunisian international revealed details of the invitation to watch Barcelona in action, but he was not allowed to attend as the president and manager asked him to remain in Toulouse for first-team training.
"I almost went but the coach and the president asked me to stay so I could be at training the following day."
Abdennour can play at left-back or centre-half and the former-Werder Bremen star has 10 caps for Tunisia.
And the 23-year-old could be sold in the summer if Toulouse's economic problems worsen, according to reports in France.
Abdennour's agent, Abdelkader Jilani, told Shems FM recently: "Toulouse are very close to Barca, so recruiters from Camp Nou often come to Toulouse and they know Abdennour very well.
"Abdennour will definitely join a top European side whether it's Barcelona or not."
Arsenal have struggled defensively this season, although recent back-to-back clean sheets hint at improvement.
The Gunners could be in the market for a new centre-back in the summer, while Manchester City may be looking to add competition to their current defensive rotation of Kolo Toure, Matija Nastasic, Vincent Kompany and Joleon Lescott, especially if Roberto Mancini continues to experiment with his 3-5-2 formation.
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