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Former Watford boss Flores, currently in charge of La Liga club Espanyol, is one of several candidates that the Potters are looking at.
The ex-Real Madrid defender spent one season in charge at Vicarage Road, leading the Hornets to 13th place in the Premier League and the semi-finals of the FA Cup, before effectively being sacked in May 2016 when they decided not to extend his contract.
His deal with Espanyol runs until the end of next season, but it is understood that he would be interested in a return to the Premier League.
Stoke have had to rejig their managerial wanted list after Gary Rowett signed a new deal on Tuesday night to stay in charge at Derby until 2021.
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O’Neill remains on that list, potentially as a short-term option, and could combine the role with his job as Republic of Ireland boss until the end of the season.
The former Leicester, Aston Villa and Sunderland manager verbally agreed a two-year contract extension with the FA of Ireland before their World Cup play-off defeat by Denmark in November, but has yet to sign it.
Stoke are expected to make contact with O’Neill, although he’s not thought to be their first choice for the job.
The Potters still hope to have a new man in place in time for Monday’s Premier League trip to Manchester United, having sacked Mark Hughes last Saturday.
First-team coach Eddie Niedzwiecki has been in caretaker-charge this week, with both Hughes and his assistant Mark Bowen leaving the club after last Saturday’s humiliating FA Cup exit at the hands of League Two side Coventry.
The Potters have fallen into the Premier League relegation zone after collecting just four points from their past seven matches.