Relations between the two countries reached a new low Wednesday when Turkey forced down a Russian airliner allegedly carrying weapons intended for use by the Syrian government in its 18-month battle with rebels, the BBC reported.
Brahimi will meet with Turkish Foreign Minister Ahmet Davutoglu, a day after meeting with Saudi Arabian officials in Jeddah.
Brahimi may travel to Damascus next week.
Seizure of the Russian plane followed shelling of a Turkish border town by Syrian forces two weeks ago that killed five civilians, CNN said. Turkey retaliated by attacking a Syrian military base near the border.
Only two years ago Turkey and Syria enjoyed a close relationship, even allowing unrestricted travel over the border. That changed after the start of the fighting inside Syria. Turkey's Prime Minister Recep Tayyip Erdogan accused Syrian President Bashar al-Assad of massacring his own people. Syria charged that Turkey was arming and financing Syrian rebels.
More than 93,000 Syrian refugees are living in camps in Turkey.
Fighting between the rebels and Syrian forces continues in several cities, Voice of America reported.
On Friday, they battled for control of a government air defense base near Aleppo. Reports are conflicting as to whether the rebels seized the base.