The La Liga giants have been in negotiations to sign the Liverpool ace since losing Neymar to Paris Saint-Germain in a €222m (£202m, $260m) world-record transfer.
Coutinho typically plays as a left winger in Jurgen Klopp's 4-3-3 formation but it has been said that Barcelona want him to become the long-term replacement for Andres Iniesta in Valverde's midfield.
But the Liverpool star's move to the Nou Camp has come into doubt after a number of reports claimed over the weekend that Barcelona are closing in on the signing of Seri from Nice in a €40m deal.
Seri is a creative midfielder and those reports come days after it emerged that Liverpool had rejected an offer worth around €130m from the Catalans to part ways with Coutinho.
Valverde, however, has failed to confirm whether the two pursuits are linked.
"I do not know if they [Seri and Coutinho] are compatible," Valverde said in the press conference following the Catalans 2-0 victory over Real Betis in the first La Liga game of the campaign.
"I can speak about the players I have here but not about the ones that I don't have in my squad. I can't tell you whether they are compatible or incompatible. I don't know."
Valverde has lost Neymar to PSG this summer and claimed that he doesn't want more scares this summer, following recent reports claiming that Lionel Messi could follow in the same footsteps to join Manchester City.
"Until the market shuts, the rumours won't stop, the Barcelona boss said. "We've had enough scares this summer and we don't want any more of them..."
Meanwhile, Valverde explained his decision to use Messi as a false nine during the win over Betis, claiming that he is still trying to find the best solution to fill the huge gap left by Neymar in his attack.
"In the end, no matter how you play or with which formation, the style is still the same. We have lost some depth with Neymar's departure and we need players to make the pitch wider for us. We had [Gerard] Deulofeu and Paco Alcacer to do that. But anyway we must always be together to help each other and be well organised in defence," the Barcelona boss explained.
"[Using Messi as a false nine] it is one of the possibilities that we looked at to take advantage of the speed of Paco and Deulofeu in wide areas. We already tried it in United States [during pre-season] and I thought it helped us as overall we were good and dominated the game. It is one of the possibilities that we have but I'm not going to tell opposing teams all of our plans but it is an advantage for us that we can use."