If confirmed, it would mark a rare case of contact in the conflict between the Damascus regime and the rebels seeking to oust it.
The Hurriyet newspaper likened the zone to the demilitarised "Green Line" in Cyprus between the Turkish Cypriot and Greek Cypriot communities.
The corridor has been set up in the south of Al-Bab and varies in width from 500 metres to 1,000 metres (yards), Hurriyet said, adding that occasional communication took place between the rival sides.
There has been intense fighting between Turkey-backed rebels and IS jihadists to take full control of the northern Syrian town.
President Recep Tayyip Erdogan said Sunday that Turkey-backed forces had entered the centre of Al-Bab and that its capture was imminent.
Hurriyet said rebels now controlled 40 percent of the town.
Meanwhile, Assad's forces have pushed towards the town from the south, completing an encirclement of the IS fighters.
Turkey has been an implacable foe of Assad since the start of Syria's nearly six year civil war, backing the rebels who sought to oust him from power.
But in the past few months Turkey's relations with Assad's main ally Russia have warmed dramatically and Moscow and Ankara have been working together to bring peace to Syria.
Ankara has always vehemently denied sporadic reports of secret political contacts with the Assad regime.
Backing the opposition fighters, Turkey launched an unprecedented incursion inside Syria in August, taking back several border towns including Jarabulus and Al-Rai from the jihadists.
But the battle for Al-Bab has proved the toughest in the campaign that claimed at least 67 Turkish troops' lives, according to tallies.