The Hurriyet daily said the attacker - who has yet to be formally identified and remains on the run - showed signs of being well trained in the use of arms.
He wreaked havoc inside the Reina nightclub on New Year's night early Sunday, spraying some 120 bullets from his Kalashnikov before disappearing into the night.
The IS extremist group on Monday claimed the attack, the first time it has clearly stated being behind a major attack in Turkey.
Hurriyet's well-connected columnist Abdulkadir Selvi said the attacker had been identified, with investigators focusing on the idea he was from Central Asia.
He said he had been trained in street fighting in residential areas in Syria and used these techniques in the attack, shooting from the hip rather than as a sniper.
The attacker had been "specially selected" to carry out the shooting, he said.
Deputy Prime Minister Numan Kurtulmus said on Monday that the authorities had obtained fingerprint data about the attacker and expressed hope he would be "speedily" identified.
Selvi wrote the priority now was to detain the assailant and neutralise the cell that apparently backed him, in order to prevent any new attack.
"This specially trained terrorist has still not been detained and is still wandering dangerously amongst us," he wrote.
He said that an IS attack was also planned in Ankara on New Year's night but that it had been prevented after eight IS suspects were arrested in the city. There were no further details.
In a separate report, HaberTurk daily said the attacker had arrived in Istanbul from the southern city of Konya with a woman and two children "so as not to attract attention".
