The man was identified by police on Sunday as a 34-year-old Uzbek who is part of a Central Asian Daesh Takfiri terrorist cell, the Hurriyet daily and other Turkish newspapers reported.
The attacker, who remains on the run, has the code name of Ebu Muhammed Horasani.
There has been no official confirmation of the reports.
Initial reports had said the attacker was a Kyrgyz national. Later reports said it was an Uighur from China.
Last week, Turkish police released images of the alleged attacker, including a chilling silent video he purportedly took in central Istanbul with a selfie stick.
The pro-government Yeni Safak daily, citing security sources, recently reported that the attacker was believed to be hiding in a house in Istanbul.
Armed with a long-barreled weapon, the assailant first killed a policeman and a civilian outside the club before entering and shooting at some of the nearly 600 people inside.
The gunman is suspected to have known in advance that the guards at the club were not allowed to carry weapons.
Turkey has been hit by numerous acts of terror over the past year. Daesh has claimed most of the assaults.
The country has long been viewed as a safe transit route for Takfiri militants, including Daesh terrorists, into Syria. Ankara stands widely accused of providing support to the militant groups operating against the government in Damascus.