Prof. Demir in Apr 2021 mentioned exactly that plan and he was even talking about TCG AnadoluTAI has got their eye on Hurjet to be navalised going forward. This has been mentioned by several officials. As a trainer and especially as an acrobatic plane
“We have been working on making changes in the design of Hürjet to operate on naval assets. We carried out several designs and made simulations. It has been seen that the design of its current form can evolve in this direction. The studies are also ongoing; the aim is to evolve Hürjet into a shipborne aircraft to operate it from TCG Anadolu.”
After this TAI Manager stated that TAI has been in talks with the Turkish Navy about operating Hürjet on LHD Anadolu, and they plan to make a protocol with the Turkish Navy to keep cooperation on this issues.
He also emphasized that the Hürjet can land and take off from a carrier and meet the operational needs of the Turkish Navy.
“Several systems would be integrated into the aircraft to make it adaptable with naval assets.” the aircraft program manager added.
Turkey Plans to Deploy Indigenous Aircraft 'Hürjet' on LHD Anadolu - Naval News
After Turkey was taken out of the F-35 aircraft program because of CAATSA sanctions imposed by the United States, it has been trying to develop new solutions to deploy fixed-winged air assets on Landing Helicopter Dock (LHD) Anadolu.