Cockerill cited a difference of opinion with Georgia Rugby Union (GRU) president Davit Kacharava as an underlying factor behind him stepping down.
Gatland isn’t the only coach in consideration with Midi Olympique reporting the GRU is pursuing former Perpignan coach Franck Azéma, although it adds a “New Zealand coach is also under consideration.”
Since leaving Wales, Gatland has worked in an advisory role with Uruguay’s professional club side Penarol for the Super Rugby Americas.
Last month, The Rugby Paper reported Gatland was considering taking up a similar role with Los Teros through to the World Cup.
He was one of Wales’ most successful and longest-serving coaches during his first 12-year spell in charge, when he recorded 70 wins in 125 games and led them to two grand slams and two World Cup semi-finals between 2007 and 2019.
He also coached the British & Irish Lions in 2013 and 2017 during this time, the latter ending in a drawn series against the All Blacks.
Gatland then coached the Chiefs before moving into a director of rugby role and then being recruited back to Wales, where he recorded six wins and 20 defeats.