The team, last in the championship without a point, said in a statement that current principal John Booth and sporting director Graeme Lowdon are leaving at the end of the season.
Wurz, who announced earlier in the week that he was hanging up his helmet after the coming world endurance championship finale in Bahrain, told the BBC he had been approached.
"I would have preferred it not be out in public but I can't deny it," added the 41-year-old former McLaren driver, without saying whether he would accept the principal role.
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Ryan resigned as McLaren sporting director in 2009, after 34 years with the team, following a furore in which he and the team's then-world champion Lewis Hamilton were found to have misled race stewards in Australia.
Manor said Ryan, who is now 61 and has spent the last six years running his own sportscar team, would be joining with immediate effect.
The team are switching from Ferrari to Mercedes engines next season and owner Stephen Fitzpatrick said Ryan's arrival was "another important step towards our goal of creating a truly competitive racing team."
There is one race in Abu Dhabi remaining after this weekend's Brazilian Grand Prix and Ryan said he was excited to be back in the paddock.
"Having spent time with Stephen and understood his vision for the future, it is clear he has ensured there is a strong platform from which the team can make big steps forward in the seasons ahead," he said.
"There is clearly a big challenge ahead and a lot of work to do, but I can't wait to meet the wider team and get down to business."
Manor entered Formula One as Virgin Racing in 2010 and were then transferred to Russian ownership, becoming Marussia.
They then hit financial hard times and went into administration last year, missing the final three races.
Fitzpatrick, who runs Independent British energy supplier Ovo, took over as owner in March with the team benefiting from an estimated $50 million in prize money after finishing ninth last year.
That was due to the efforts of French driver Jules Bianchi, who died this year after suffering severe head injuries in a crash in Japan last October.
(Reporting by Alan Baldwin; Editing by Frank Pingue)
