The Croatian veteran came close to moving to Manchester United over the summer and remains available.
TMW says Mandzukic is in contact with Al Gharafa and Al Rayyan. Al Duhail were also interested, but their foreign spaces were already filled.
Al Gharafa and Al Rayyan are both keen, with talks centred around a €5m salary.
Any move, however, will be dependent on the approval of the government's Ministry of Sport.