Ajax coach Martin Jol has turned down the job at Fulham.
The 54-year-old told the Cottagers earlier in the week that he was ready to take over the hot seat vacated when Hodgson left for Liverpool.
But Ajax have assured Jol of their ambition and promised him transfer funds, which has convinced the former Tottenham Hotspur manager to stay at the Amsterdam Arena.
Jol said: "Ajax let me know they didn't want me to go. And I don't think I can bring myself to leave Ajax at this time.
"I came here last summer to be successful, to build a good team and to have fun. And those three things are what I am interested in achieving next season.
"It was always my intention to build Ajax further. It is full speed ahead and we all need to roll up our sleeves. That is essential."
He added: "I received offers from other clubs in April and May, and I brushed them aside, but this time my agent Mino Raiola held serious talks with the British delegation.
"I am pleased that these hectic days are over. Together with the club I am looking to the future. We now have a priority and that is Wednesday's (Champions League) game against Panathinaikos."
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