Gary Rowett was perceived to be the favourite before he signed a contract extension with Derby County leaving O'Neill and former Watford manager Sanchez Flores in the frame.
Balague, a well-respected Spanish journalist, claims the current Espanyol boss has already met with the club's board over a potential deal.
Stoke managerial target Quique Sanchez Flores has committed his future to Espanyol amid heavy speculation that he is to be the next Stoke manager.
Sky Sports football expert Guilleme Balague says Quique Sanchez Flores has been given until Friday to make up his mind over becoming the new Stoke manager. "I am the coach and will be", he said.
'I belong to Espanyol.
'We feel happy. We are in a happy place and we don't want to break that up'. I am well and quite happy with my situation.
"O'Neill has still not decided whether to accept their offer as he and his assistant Roy Keane are excited by the challenge of building a new, younger Ireland squad during their European Nations Cup campaign, which starts later this year", writes Edwards.
Martin O'Neill is the frontrunner to take over at the bet365 Stadium, with Stoke travelling to Manchester United on Tuesday (AEDT). The Potters, who now sit 18th in the Premier League table, face Manchester United on Monday night.