For starters, it has a Chinese radar. I would very much like our AAMs to be as far as possible from any Chinese radars. We know however that Roketsan and GIDS are working together on new AAMs. Those could be deployed on Azerbaijani JF-17s as well.
If iirc, there was an option of Vixen-1000 for JF-17C from Leonardo. Though Azerbaijan probably has to pay for integration cost.