The Sunday Times says Mislintat was unhappy with Emery's decision to sign Suarez in January.
The German joined the Gunners in November 2017 after a successful spell with Borussia Dortmund but left after just 14 months.
During his time with the Premier League club, Mislintat played a key role in bringing several big names to the Emirates including Pierre-Emerick Aubameyang, Bernd Leno, Lucas Torreira and Matteo Guendouzi.
However, Mislintat was 'dismayed' by Emery's decision to sign Suarez on loan from Barcelona during the January transfer window, with his departure coming shortly after.
The German was disappointed by the move because he wanted to give more opportunities to some of Arsenal's academy players who played in the same position, notably Joe Willock and Bukayo Saka.