The body of the Russian will be prepared in accordance with tradition before being given to Moscow, Xinhua quoted Davutoglu as saying in Ankara before his departure for the EU-Turkey Summit.
Two Turkish F-16s downed the Russian jet on November 24 alleging it had intruded into Turkish airspace. Moscow has denied any intrusion, saying it was engaged in bombing IS rebels in Syria.
The pilot and the navigator ejected safety, but the pilot was shot dead. The navigation is in a Syrian hospital.
Davutoglu said while Turkey was sad the incident had taken place, similar disasters could happen unless there was information sharing and coordination.
On Saturday, Turkish President Recep Tayyip Erdogan said: "We feel really sad about this incident. We would not like such a thing to happen, we would not want it but unfortunately it did. I wish such a thing will not happen again.
"What we tell Russia is 'Let's talk about this issue within its boundaries and let's settle it. Let's not make others happy by hurting our relationship," he said.
Erdogan had previously sought a meeting with his Russian counterpart Vladimir Putin on the sidelines of the climate summit meeting in Paris but Kremlin rejected the request.
Turkey-Russia relations have plummeted after the shooting down of the Russian.
On Saturday, Putin imposed economic sanctions against Turkey.
Accordingly, Turkish transport companies shall be restricted in their operations in Russian territories. Turkish ships and boats are banned from staying at or navigating across Russian ports. Import of certain goods from Turkey will be halted.
Russia also officially suspended its visa-free travel regime with Turkey, except for Turkish diplomats and their dependents.