"I've developed a very interesting relationship with him," the triple Olympic champion said in an interview with French weekly Journal du Dimanche.
"I've worked with him for seven years, which has given me an opinion that is a little different from the one that is widely circulated," said Killy, head of the Coordination Commission for the 2014 Winter Olympics to be held in the Black Sea resort of Sochi.
Killy, 70, said "everything is going marvellously well" in his dealings with the Russian strongman. "You can get ahold of him in a minute just by calling his chief of staff."
"The Putin I know is not the one described in the newspapers, where you see real 'Putin-bashing'," he told the paper.
"I have no reason to follow the crowd; I trust what I see. When he calls me from Moscow at three in the morning his time to wish me a happy birthday, I find that nice."
He added: "When he plays sad tunes on the piano at the end of an evening with 10 ministers singing along, that's not hum-drum."
The run-up to the Winter Games to be held in Sochi from February 7 to 23 has been marred by controversy, notably over a law against "gay propaganda" that Putin signed in June.
Critics say the vaguely worded legislation, which punishes the dissemination of information about homosexuality to minors, can be used for a broad crackdown against gays.
The law sparked calls from campaigners and celebrities such as British actor Stephen Fry to strip Russia of the Winter Games.
"Putin told me of his surprise over the reactions and the amount of fuss it caused," Killy said. "He told me he recently bestowed a literary prize on a homosexual. For him, it is not an anti-gay law."