Those rumours were strongly denied by Mourinho on Friday, the United boss claiming he has "never been so happy" with the World Cup winner.
Pogba will retain the United captaincy for Sunday's Premier League game at Brighton but rumours over his long-term future continue to swirl.
Barca have been touted as a potential destination for the France midfielder, with Valverde looking to fill the gap left by departing club icon Andres Iniesta.
But ahead of Saturday's La Liga opener at home to Deportivo Alaves, Valverde swerved questions about the club's reported interest in Pogba.
"We do not get into discussions about players of other teams," Valverde told reporters at a news conference.
"We want them to respect our players and we respect those of others."
Barca have signed uncapped Brazilian pair Malcom and Arthur in preparation for their title defence, while Arturo Vidal has joined from Bayern Munich.
And while Valverde is open to concluding more deals ahead of the transfer window's closure, he is satisfied with the squad at his disposal if there are no further arrivals at Camp Nou.
"I do not stop to compare squads with the previous ones, but I have some extraordinary players," Valverde added.
"We do not know if the squad is closed or not. We have a good team to face what's coming, but there's still time.
"The markets are closing, there are many rumours... but here we will continue until August 31. I'm happy with what I have."