It is also understood that Republic of Ireland manager Martin O'Neill is under consideration for the manager's job at the bet365 Stadium.
Sánchez Flores is under contract at Espanyol until the end of the current season, with the option of another year on the table if all parties agree.
Balague said a five-year proposal from Stoke would tempt Flores after a tenure of broken promises at Espanyol.
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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?
Sanchez Flores refused to comment on the speculation last night after his team defeated Levante to reach the Copa del Rey quarter-finals, but the former Watford, Benfica and Aletico Madrid boss now looks likely to confirm his desire to manage the Potters.
"I don't want to talk about me, but to enjoy these moments".
Stoke, who are now 18th in the Premier League, face Manchester United at Old Trafford on Monday night and they reportedly would like to have their new man in place by then.