The fighter jet that the Azerbaijani air force can reach by the shortest route is the Pakistani JF-17. However, this agreement could not be formalized. There has been a lot of speculation about reasons, as most of you know...
Anyway, Azerbaijan is now semi-officially part of the KAAN program. And they will also acquire the Hurjet as advanced trainer for KAAN. As far as I can understand, in order for the JF-17 to find a place for itself in the 'non-Russian' new air force structuring , they want it to serve smoothly in the same infrastructure with these near future platforms. For this reason, it has been speculated in the past that there may be some evaluations on the possibility of partial privatization and create an variant of the JF-17. Many air forces can operate east and west jets at the same time, but with completely different logistics lines, with vastly different training-documentation and maintenance lines... The Azerbaijani air force, on the other hand, is modeled on the Turkish air force school, and its structuring, infrastructure investments and training processes are shaped accordingly.
The modernization model created by TAI for the Georgian and later Azerbaijani Su-25s is a small-scale effort that has not received much attention, but I think is indirectly related to this issue. TAI may soon be able to make some contributions to the JF-17 that will enable it to be more robustly offered to air forces that are compatible with NATO infrastructure.