The Manchester United goalkeeper is currently on a season-long loan with Trabzonspor.
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Onana has impressed in the Super Lig, though appears to have little hope of continuing his career with United after the arrival of new No1 Senne Lammens.
The iNews says if Onana is told he has no future at Old Trafford, the Cameroon international will seek a move within the Premier League.
Trabzonspor are keen to sign Onana permanently, though his plan for the moment is a return to England next season.