Valverde's position has come under increased scrutiny after Barca's dramatic 3-2 defeat to Atletico Madrid in the Supercopa de Espana semi-final.
Al Sadd boss and Barca legend Xavi confirmed reports he had met with the Camp Nou club's director of football Eric Abidal in Qatar on Saturday (AEDT) amid speculation he will be offered the opportunity to succeed Valverde at the end of the season, or potentially before that.
But the 39-year-old was reluctant to go into detail about the meeting, insisting he respects his former club and its current coach.
"Coaching Barca is my dream, I cannot hide that, everyone knows I support them from the bottom of my heart," Xavi said after leading Al Sadd into the Qatar Cup final with a win over Al Rayyan on Sunday (AEDT).
"Yes, Abidal is my friend. I've met him many times, so I cannot say anything, just that I respect Barcelona, I respect Valverde, I respect the players, I respect my club.
"They [Barca] were here to talk to me and we discussed many things."
"They were here also to check on Ousmane Dembele, that's all," Xavi added of the Barcelona forward, who is recovering from a thigh injury in Qatar.
"I cannot say anything else. Sorry, but I cannot inform you too much. I met Abidal, he is my friend, that's it.
"I'm doing my job here, I'm doing my best. I was focused on the semi-final and now we play the final so I'm very happy. I'm very happy to coach Al Sadd and I am focused on my team."
Xavi endured a long and distinguished playing career with Barca, with his incredible list of honours including eight LaLiga titles and four UEFA Champions League triumphs.