Espanyol and former Watford boss Quique Sanchez Flores is Stoke’s first choice to succeed Mark Hughes.
It is understood a Stoke delegation met Flores in Barcelona on Wednesday, and that Republic of Ireland manager Martin O’Neill is also under consideration.
The Potters sacked boss Hughes last weekend after the 2-1 FA Cup loss at League Two Coventry, which followed a run of seven losses in 10 Premier League games.
The 18th-placed Staffordshire outfit were interested in Derby manager Gary Rowett until he signed a new contract with the Rams on Tuesday.
Flores’ one season in English football to date saw him guide Watford to a 13th-placed Premier League finish in 2015-16, with the Hornets also reaching the FA Cup semi-finals.
The 52-year-old Spaniard then took charge at Espanyol in the summer of 2016, on a three-year deal, and they finished eighth in LaLiga last term. They were 14th ahead of Thursday’s match at Levante.
O’Neill and his coaching team agreed contract extensions with the Football Association of Ireland last October.
But the 65-year-old said after the Republic lost their World Cup qualifying play-off the following month that he would need to have “a real think” about his future, and still nothing has been signed.