The 43-year-old believes the Portuguese manager’s great rapport with African players means Djiku is in good hands.
Djiku will work under Mourinho next season after the Portuguese was confirmed as the manager of Fenerbahce earlier this week.
The 29-year-old will, therefore, join a select list of Ghanaian footballers to have worked with the former Inter Milan manager, including Essien and Sulley Muntari.
The Turkish giants unveiled Mourinho as their new head coach on Sunday, with thousands of fans showing up at the Sukru Saracoglu Stadium to welcome him.
Mourinho previously worked with Essien at Chelsea and Real Madrid and also won the treble with Muntari at Inter Milan.
Appiah, who previously played for Fenerbahce, believes Djiku too would be able to take his game to the next level under Mourinho.
"Jose Mourinho has been very good with African players and I think everyone he’s worked with proves themselves including Didier Drogba, Solomon Kalou, Michael Essien, Mikel Obi and a lot of them,” Appiah told Responsible Gambling.
"We have Djiku who has been able to win the hearts of the fans with the way he carries himself around and the way he approaches the game and I hope that with the arrival of Mourinho, he will be able to take his game to the next level."
Appiah joined Fenerbahce from Juventus in 2005 and spent three years in Turkey, where he won the league and cup.
Meanwhile, Djiku has been a key player at Fenerbahce since joining the club in the summer of 2023 on a free transfer after parting ways with Ligue 1 side Racing Strasbourg.
He made 36 appearances in all competitions for the club last season, contributing three goals and two assists.