Reveillere is available on a free transfer after leaving Lyon earlier this summer.
The news has alerted a host of clubs across Europe to Reveillere's availability with the full-back boasting a wealth of experience for club and country.
Reveillere enjoyed a trophy-laden ten-year spell at Lyon, helping them to win the Ligue 1 title five times and was a regular in their UEFA Champions League campaigns.
The 33-year-old is equally adept at playing at right-back, as well as left-back, and several English sides are now weighing up moves for Reveillere.
Cardiff have been credited with an interest in Reveillere and the player's agent, Willie McKay, has confirmed several clubs have expressed an interest in the defender and that the player is keen to try his luck in England.
"Anthony is one of the best free transfers in Europe this summer and it is no surprise that a number of clubs are keen on him," Mackay told Sky Sports.
"I am speaking to several clubs about Anthony possibly coming to England and it is somewhere that Antony would like to play.
"Anthony has played at the highest level for club and country for the last ten years and he would be a massive success in the Premier League if he moved to England."