Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
Tankovic joined the London outfit in 2011 when he was 16 years of age and made his debut for the Cottagers in the 2013/14 campaign.
The 19-year-old Swede featured in three Premier League games for Fulham, but was not offered a new contract when his original deal ran out.
Dutch club AZ have now recruited Tankovic on a contract that runs until June 2019.
AZ have also signed Guus Hupperts from Roda JC, who suffered relegation from the Eredivisie at the end of last season.
The 22-year-old winger cost the Alkmaar-based club for approximately €1million and has signed a contract that runs until June 2018.