Earlier this month, it was claimed that Manchester United were prepared to activate Roberto's £36m release clause in a bid to bring the versatile midfielder to Old Trafford.
Valverde has admitted that anything is possible in the final weeks of the transfer window, but the newly-promoted manager hinted that he wants to keep the 25-year-old at the club.
"Sergi Roberto is also a very important player for us. It'd be too much to talk about what can happen. We'll be like this until August 31," Valverde told reporters.
Roberto has made 153 appearances for Barcelona in all competitions.