Turkish Chief of Staff General Hulusi Akar set out Ankara's proposals to the US Chairman of the Joint Chiefs of Staff Joseph Dunford during his visit to Turkey, Hurriyet daily said citing security sources.
Dunford travelled yesterday to the Incirlik airbase in the southern Turkish province of Adana, which is used for air raids against the Islamic State group (IS).
Turkey has repeatedly called for a joint operation with the US to clear Raqa of IS excluding Syrian Kurdish militia.
In one of the proposals, Ankara suggests Turkish and US special forces supported by commandoes and Turkey-backed Syrian opposition fighters would go down to Raqa via the Syrian town of Tal Abyad, the daily reported.
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Tal Abyad was captured by Kurdish and Arab rebels in June 2015 and is 80 kilometres away from Raqa.
The newspaper said this would mean the US would have to persuade the Kurdish groups to let the forces through to reach Raqa via a 20-kilometre corridor.
Al-Bab is IS's last stronghold in Aleppo province and the Turkish operation is currently engaged in clearing IS from the town, Turkish Defence Minister Fikri Isik said this week.
Relations between Washington and Ankara have soured over the six-year conflict as the US sees Syrian Kurdish militias as the most effective ground force against IS.
But Ankara views the Kurdish Democratic Union Party (PYD) and its armed wing, the Kurdish Peoples' Protection Units (YPG), as extensions of Kurdish separatist militants waging an insurgency against Turkey.
But it is not clear whether US President Donald Trump will continue to rely on the Kurdish militias for any operation in Raqa.
Turkish Prime Minister Binali Yildirim said it would not be right for the US to work with the PYD and YPG.
"You cannot go against a terror organisation with another terror organisation," Yildirim said, quoted by the CNN Turk broadcaster.
He said he believed the US administration would take these assessments into consideration.