The Irish boss looks likeliest to take over due to the fact he has yet to sign a new contract with the Football Association of Ireland, although Flores is weighing up what is said to have been a persuasive offer from the Stoke delegation that met him.
But Flores refused to answer questions about his future after Espanyol's Copa del Rey win over Levante on Thursday night.
"I don't want to talk about me, but to enjoy these moments".
Although with no experience at the top level, having won League Two with Northampton Town in 2016, League One in 2017 and now doing so well in the Championship, would the 50-year-old be a gamble worth taking? "I want to continue being happy with my profession".
Balague said a five-year proposal from Stoke would tempt Flores after a tenure of broken promises at Espanyol.
He added: "I'm very grateful to Espanyol, I've been frustrated sometimes because we haven't advanced as fast as desired, but that's because Espanyol haven't been able to, not because they haven't wanted to".
But there is even a suggestion in Spain that he could still be with Espanyol's for Sunday's game against Athletic Bilbao.
According to BBC Sport, Stoke have made Sánchez Flores their back-up target if a bid to bring in Republic of Ireland manager Martin O'Neill fails, the main stumbling block to that eventuality being that O'Neill will insist on combining his worldwide role with attempting to reverse Stoke's fortunes.