Le Temps said, contrary to Turkish reports, the alleged killer does not have a Swiss passport and lost his C residency permit after spending three years in a prison in Lenzburg in the canton of Aargau.
The man, described in Swiss media as a jihadist, was arrested with two accomplices, a Macedonian and German.
The three men were in a pickup truck last Thursday at a Turkish army checkpoint in the province of Nigde in the centre of Turkey when the attack occurred.
“I did a good deed by killing the Turkish gendarmerie soldier,” the man later told police, the Dogan News Agency said.
Identified by his initials, C.R., he is alleged to have killed a policeman, a soldier and another person.
Le Temps said he was originally from the Balkans and had lost his residency permit for Switzerland.
Because of the “serious risk* he posed to the security of Switzerland, he was expelled from the country and his C permit was revoked, the newspaper said.
It cited the Federal Migration Office confirming this information.
The Swiss intelligence service recently acknowledged that a “dozen Swiss jihadists” were linked to the conflict in Syria.
Le Temps said C.R., who stll has family members in Switzerland, cut ties with Switzerland six months ago.
Journalists from Tagesanzeiger and 20 Minuten, who contacted friends of C.R., reported that he attended secondary school in Brugg in the canton of Aargau.
He landed in prison after his involvement in the armed robbery of a jewellery shop, according to reports.
A friend described how he turned to Islam while behind bars in Switzerland, the Blick newspaper said.
“This was clearly demonstrated by the fact that he let himself grow a typical, strictly religious Muslim's beard,” the newspaper said.