It's been reported that the former Watford, Valencia, Benfica and Atletico Madrid boss was the Premier League club's first choice to replace Mark Hughes and that a Stoke delegation met with the former Watford boss in Barcelona on Wednesday.
Speaking at a press conference, Flores said he "belonged to Espanol".
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.
Eddie Niedzwiecki has been in temporary charge since Hughes' departure, taking training ahead of the Monday's league trip to Manchester United.
They are third from bottom in the Premier League with 16 games left to secure survival in the top flight.
Stoke, 18th in the Premier League, hoped to agree a deal for the Spaniard, but he has opted against a return to England and will instead remain at Espanyol.
"I have nothing else to add, only that I have to focus on the next LaLiga match". I am well and quite happy with my situation.
"I don't want to talk about me, but to enjoy these moments". It's a day for Espanyol, for the club, for the players, it's a day to celebrate for having qualified for the quarters.
However, the former Watford boss has declared his intention to remain in Spain.
Balague said a five-year proposal from Stoke would tempt Flores after a tenure of broken promises at Espanyol.