The three clubs have made enquiries to Ozer's representatives regarding his current situation and availability.
Ozer is viewed as an investment for the future and would be loaned out if he were to leave Fenerbahce to gain first-team experience.
The 19-year-old joined the Turkish club from the highly-acclaimed Altinordu academy as one of the top talents in Turkish football.
Ozer turned down interest from several European sides including City, Liverpool and Basel to join Fenerbahce under the impression he would be joining a club prepared to give him a role in the first team.
But the young keeper made just one appearance in the Turkish Cup in what was a disappointing season for the Super Lig giants.
The Yellow Canaries fired former manager Phillip Cocu in December and replaced him with Ersun Yanal, who helped them secure a sixth-place finish after briefly hovering above the relegation zone at the turn of the year.
Ozer could struggle to progress in the first team next season under the stewardship of Yanal after Fenerbahce signed 21-year-old keeper Altay Bayindir from Ankaragucu.
Fenerbahce have traditionally not favoured youth but their policy was expected to change in the Ali Koc era.
Additionally, the Istanbul-based club have Harun Tekin currently ahead of Ozer in the pecking order while veteran keeper Volkan Demirel may also sign a contract extension, with the club expected to hold a meeting with Ozer and his representatives over his future.
Ozer has already been called up to the senior Turkish national team on two occasions but has yet to make his debut.
Fenerbahce traditionally do not have the best track record when managing young talents, a fact that is best illustrated by former academy product Merih Demiral.
Demiral left the club for the Portuguese third-tier in fear of his career not progressing in the Fenerbahce academy. Sporting CP snapped him up before his move to Alanyaspor last summer.