The Monaco defender has been the subject of interest from several clubs this summer.
The powerful centre-back is believed to be a target of West Ham United, Newcastle United and Liverpool, as reported by the Daily Mail, but he could now be heading to La Liga after Atletico made their move .
The report claims Atletico have approached Monaco with an initial bid of around £11 million, but the French club are believed to want upwards of £14 million for his sale.
Meanwhile, the Spaniards are said to have initiated contract talks with Abdennour’s representatives over terms, with a five-year deal and net salary of £1.07 million the rumoured details.
There is still some way to go if Atletico are to reach a deal but following the sales of centre-backs Miranda and Toby Alderweireld, the pressure is on to find a partner for the ever-present Diego Godin.
The Tunisian's Premier League suitors could still be in with a shout, however, and will hope that the disparity between the bid received and the fee demanded by Monaco will allow them to sneak in.