Smullen, 33, was installed as favourite to take over as No 1 to Aidan O'Brien and the Coolmore horses following Murtagh's surprise statement on Monday that he was stepping down.
However, Smullen, Ireland's champion rider, is to remain as stable jockey to Dermot Weld. "I've got a very good job and I ride for some very good owners so I'm happy where I am," he said. "I'm staying with Dermot and very happy to do so. He's a world class trainer and he's got some great owners. I'm very happy in the position I am at the moment."
Paddy Power make Belgian Soumillon even-money to get one of the biggest riding jobs in racing, but have also seen some interest in French-born former US champion apprentice Julien Leparoux, and introduced him into their betting at 10-1.
Paddy Power said: "We were contacted this morning and asked for a price about Julien Leparoux. The inquiry came from someone whose judgment we respect and Leparoux won the same Eclipse award as Steve Cauthen and Cash Asmussen did as an apprentice.
"Later we saw a spate of cash for Christophe Soumillon at 5-2 around the time of Dermot Weld's statement that his jockey would be staying put and had to cut him to evens."
William Hill reacted to the news by removing Smullen, the previous 6-4 favourite, from their betting. Soumillon now heads the market at 15-8, although there has been money for a dramatic return to the role for Kieren Fallon who is 9-2.
William Hill's Tony Kenny said: "Christophe Soumillon is the new favourite for the job, but we've seen more money for Kieren Fallon and Colm O'Donoghue this morning."