The site links Warner Bros.' choice of Alfonso Cuarón, a relatively obscure director prior to helming Harry Potter and the Prisoner of Azkaban, with their report. Nair directed 2001's Monsoon Wedding and the just-released Vanity Fair.
When contacted by HPANA, an intern at Nair's offices in New York said she wasn't aware of any such announcement, but now The Times of India has quotes from the director saying she read the book over the weekend and is "still deciding":
I never let fame go to my head: "I'm getting offers to direct Harry Potter and the Order of the Phoenix. I read it over the weekend. I'm still deciding... I'm not letting all this go to my head. I'm grounded. I practise detachment, it helps me keep my balance. I'm a Dilliwalli [someone from Delhi], only an asana [a position in Yoga] gets me on my head! My son Zoharan's excited. I've seen all the Harry Potter movies with him."
Thanks to OdFHP.com and our own Geri for the tips.