The 37-year-old represented the club between 1997 and 2013, famously helping the side to win the 2000 Caf Champions League and Super Cup.
“I’m ready and active enough to return to the pitch and play for my darling club, Accra Hearts of Oak," Adjei told ATL FM.
“What I am now waiting for is to get an official invitation from Hearts management and the technical team for training assessment before we enter into contractual terms.
“In fact, as I’m talking to you now, I can assure you that I have had enough training and stamina which when Hearts invite me, I will not disappoint my fans.
“Even Medeama recently wanted to offer me an outright contract but I wanted them to let me have training exercise with them before the contractual terms which they didn’t like.
“Right now, I can tell you that some section of the Hearts fans came to my house last week and pleaded that I should return to the club and I told them I’m ever ready to serve the club but I can’t join the team whiles the management and the technical team have not asked me to join them, so I’m still waiting for Hearts to officially invite me to train with team."
Having joined the Phobians in 1997, Adjei transferred to Tunisian outfit Club Africain in 2004, before returning for a second spell in 2005.
He later joined Israeli side FC Ashdod before making a second return, after which he was released in 2013 following the arrival of coach David Duncan.
He was Ghana's first choice goalkeeper at the 2002 Africa Cup of Nations as well as the qualifiers for the 2006 Fifa World Cup.