The 29-year-old is, therefore, set to join a select list of Ghanaian footballers to have worked with the former Chelsea manager, including Michael Essien and Sulley Muntari.
The Ghanaian centre-back later took advantage of the off-season and jetted off to a resort in Mauritius to holiday with his wife, Heley.
However, he is now back in pre-season and will be assessed by Mourinho, who is said to be a huge fan of the defender.
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.
The former Bastia rearguard is expected to play a huge role under Mourinho next season as Fenerbahce aim to wrestle back the Turkish title from rivals Galatasaray.
Meanwhile, ex-Ghana captain Stephen Appiah has said, like Essien, Alexander Djiku could also take his game to the next level by working with Mourinho.
Mourinho previously worked with Essien at Chelsea and Real Madrid and also won the treble with Muntari at Inter Milan.