Bookies Paddy Power say the bets are in, and Givenchy's Riccardo Tisci is the winner, with odds of 8/11 (on 1 March, he was the 3/1 favourite). Next in line is Alber Elbaz with odds of 9/2, followed by Roland Mouret with odds of 5/1.
"We're not sure if it was the unconfirmed rumours that Tisci had the job driving the betting but it certainly looks like the job is his!" says Paddy Power spokesperson, Sharon McHugh.
Tisci, known for his romantic sensibility, has been a top contender from the start, in part because Givenchy, like Dior, is owned by LVMH.
"Tisci is well connected in the Paris fashion world, with close ties to French Vogue," said The Guardian. "Were Tisci to land the role, it would be a case of history repeating itself: Galliano was at Givenchy before getting the Dior job."
As for who would replace Tisci at Givenchy? Olivier Theyskens takes the top spot with odds of 11/4 - but we'll wait until Dior makes an official announcement before we place our bets.
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