Early discussions were encouraging, but they will now turn their attention back to Republic of Ireland boss Martin O'Neill after Flores' change of heart.
The club were willing to pay £1.7million to release No 1 target Gary Rowett from his contract with Derby, but the former Birmingham manager instead signed a new deal with the high-flying Championship side.
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New Jersey has one of the worst-funded pensions in the country, with a liability estimated at about $80 billion to $90 billion. Christie was a short-list finalist to be Trump's running mate, before Trump picked now-Vice President Mike Pence.
It is understood a Stoke delegation met Sanchez Flores in Barcelona on Wednesday and it had been reported that the 52-year-old Spaniard had been offered a five-year contract by the Premier League club.
Speaking at a press conference, Flores said he "belonged to Espanol". "Clubs are interested in players and coaches, and this is a lifetime".
"I live in a big city, in one of the best leagues, and I have reason to be happy and not to live anxious". "We feel happy. We are in a happy place and we don't want to break that up".
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Stoke held talks with Sanchez Flores this week but the ex-Watford manager said on Saturday: "Here I have all I need. I don't have to explain anything else".
"We like how they treat us, what we generate in the stadium and that Espanyol will grow".
Since the departure of Hughes and his assistant Mark Bowen, first-team coach Eddie Niedzwiecki has been in temporary charge at Stoke, taking training ahead of Monday's league clash with Manchester United at Old Trafford.
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Jordan Henderson (hamstring), Alberto Moreno (ankle) and Daniel Sturridge (muscle) all remain out with their respective injuries. They have lost just twice so far - the lowest number of defeats in the Premier League this season (not including Man City).