Essien is currently based in the Eastern European country, where he plies his trade as a player and manager at Sabail FK.
The former Chelsea star recently met with Giggs at a programme held in the Azerbaijani capital of Baku.
The Ghanaian played against the Welshman several times during a time when Manchester United and Chelsea held a great rivalry.
While Essien helped the Blues to some wins, Giggs had the last laugh when Man United beat Chelsea in the final of the 2008 Champions League.
Giggs played for the Red Devils all his life before calling time on his football career in 2014 to venture into management.
The 46-year-old is currently the manager of the Wales national team and has already qualified The Dragons for EURO 2020.
In an Instagram post, Essien said it was great to meet Giggs again and described the former Man United winger as a legend.
“It was great meeting you again, Ryan Giggs. Legend,” Essien wrote, accompanied by a photo of himself and the Welsh star.