Ekaterina Doronin, the estranged wife of Russian billionaire Vladimir Doronin, has been quietly searching for luxurious digs in the Big Apple, sources say. The budget, we hear, is about a cool $14 million. Reports have said the Doronins are getting a divorce after 24 years of marriage. Vlad has been dating Naomi Campbell since 2008, and — even though he started dating the model after they separated — Ekaterina will reportedly cite Campbell in a divorce filing. [Page Six]