President Recep Tayyip Erdogan said on July 2 that Syrian refugees in the country would be offered nationality "if they want it", the first time such an idea had been proposed at the highest level.
Nationality would be given step-by-step, with initial plans for 30,000 to 40,000 Syrians gaining citizenship, the Haberturk daily said.
In total, Turkey is targeting giving Turkish citizenship to up to up to 300,000 Syrians, it added.
Turkey is hoping such a move would allow skilled Syrian refugees to become citizens, the paper said. Educated refugees from other countries could choose to become nationals as well.
Family members of those chosen to become Turkish citizens could also get the right to become nationals, it added.
The usual obligation of living in Turkey for at least five years before gaining citizenship could be waived for Syrians, Haberturk said.
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Syrian refugees who become Turkish nationals would then be able to vote in elections one year after being awarded nationality.
The report appeared to generate anger among many social media users, with #suriyelilerehayir ("No to Syrians") the top trending topic in Turkey on Twitter on Saturday.
Erdogan has championed an "open door" policy for Syrians fleeing the over five-year civil war in their country. More than 2.7 million Syrian refugees now live in Turkey where they have guest status, according to the Turkish government.
The proposal to grant Syrians citizenship comes after a widely-praised move by Turkey in January this year to allow Syrian refugees to be given work permits.
Turkish media this week quoted labour ministry statistics as saying 5,502 Syrians had been granted work permits since the scheme was adopted.
Activists have accused Turkey of effectively shutting its borders to any more Syrians this year but Ankara insists it will always take in those wounded and fleeing danger.
In March this year, Turkey signed a deal with the European Union to stop refugees making the dangerous route from its western border to Europe via Greece which has led to a reduction in the number of boats leaving Turkey.