The 29-year-old goalkeeper was loaned to the Turkish side from Manchester United, where he was replaced by Senne Lammens.
Onana has made a positive impression in his four games for Trabzonspor, keeping one clean sheet and conceding five goals, while also providing an assist.
According to reports, Trabzonspor has informed Onana of their intention to sign him permanently next summer, but a fee will need to be negotiated with Manchester United.