"After a period of consideration, I have informed (owner) Stephen Fitzpatrick that I have taken the decision not to make myself available to Manor, the 41-year-old ex-Formula One driver told the BBC on Wednesday.
Manor will have a vacancy after next week's season-ending Abu Dhabi Grand Prix, with current principal John Booth and sporting director Graeme Lowdon resigning after reported differences with Fitzpatrick.
The British-based team last week appointed former McLaren veteran Dave Ryan as their new racing director.
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Wurz, who is retiring from motorsport as a driver after this weekend's World Endurance Championship finale in Bahrain, had discussed the principal role with Fitzpatrick without a formal offer being made.
(Reporting by Alan Baldwin, editing by Toby Davis)
