Barca CEO Oscar Grau and sporting director Eric Abidal met the former midfielder for talks in Qatar on Friday as pressure mounted on Valverde following the Catalans' Spanish Supercopa defeat to Atletico the previous night.
Al Sadd's sporting director then confirmed negotiations between the 39-year-old and Barca ahead of the Qatari side's cup clash with Al Rayyan on Saturday and afterwards, Xavi admitted it was his dream to coach the Catalan club one day, but said he respected Valverde.
Following further talks on Sunday morning, Standard Sport understands that Xavi will not join Barca straight away and that he told Abidal and Grau that he would prefer to take over in the summer.
For now, the Al Sadd coach is focused on preparing next Friday's Emir of Qatar Cup final and Valverde is expected to take training as normal on Monday after giving his Barca players the weekend off.
Valverde is said to be angry and upset at his treatment by the Blaugrana, but is not considering resignation at the moment and will start preparation for next Sunday's LaLiga match at home to Granada.