Vidal has slipped down the pecking order since Frenkie de Jong's arrival from Ajax, prompting speculation over his future at Camp Nou, where he has only started four LaLiga matches this season.
The 32 year-old Vidal has been heavily linked to a reunion with former Juventus head coach Antonio Conte at Serie A side Inter, while struggling Premier League giants United are reportedly interested.
Valverde addressed the rumours ahead of the Supercopa de Espana semi-final against Atletico Madrid in Jeddah, Saudi Arabia.
"We're not thinking about him going to another team," Valverde told a news conference. "We'll see tomorrow [Thursday]. In principle he's with us. No clues."
Pressed on reported interest from England and Italy, Valverde replied: "Arturo Vidal plays for us and tomorrow he'll be on the pitch or on the bench.
"We don't pay any attention to other clubs being interested in our players."
Vidal swapped Bundesliga champion Bayern Munich for Barcelona in 2018 and the Chilean has since won LaLiga and the Supercopa de Espana.
He has scored six LaLiga goals in 15 matches this season, while the veteran has amassed 20 appearances across all competitions.