Galliano was sacked from the French fashion house earlier this year after he allegedly made anti-Semetic remarks in a Paris cafe and Alaia was offered the job of helming the label, but decided it wasn't for him.
Journalist Vanessa Friedman reported in the Financial Times newspaper: "Mr. Alaia wasn't interested. Flattered, but not about to pursue. The story of what happened with John was a sad story, he said when I asked him, and he didn't want to be part of the next chapter. And that's even before you got to the other stuff."
Alaia is not the first designer to be linked the creative director post at Dior.
Riccardo Tisci - head of Givenchy - is also in the running and refused to confirm in recent interview what his future holds.
He said: "I don't know what will happen. Sincerely, I feel sorry for John. But for this moment I am leaving aside all the gossip of 'I am going here, I am going there,' because there is a lot of gossip circulating and there always will be. I will tell you, In This Moment, I am very happy at Givenchy and it is a moment in which I am bringing The Game to the next level. So I tell you, I feel at home. It's as if it were my son. I don't know how to explain it. It would be very difficult for me to leave."