The 16-year-old's representative claims the Catalans offered the better financial package.
23-year-old striker has only scored seven goals in his debut campaign at the Nou Camp
Los Blancos will focus on signing Manchester United keeper David De Gea instead.
Former Sevilla wing-back suffered serious ankle injury in early February.
Valverde helped Bilbao win the Spanish Super Cup in 2015 after defeating Barcelona.
Diego Simeone needs to sign a proven top scorer to keep fighting with Real Madrid and Barcelona.
La Liga giants have reportedly agreed to pay his £38.8m release clause.
Coutinho has long been linked with a move to the Catalan giants.
The former Real Madrid keeper was linked with a move to Antonio Conte's side in the last two windows.
Barcelona finished three points behind their arch-rivals in La Liga standings.
Spanish international is said to be the Catalans' alternative to Arsenal's Hector Bellerin for the right-back.
Marca reported last month that Los Blancos have agreed personal terms with the Manchester United ace.
Manchester City, Chesea, Juventus and Barcelona had been linked with him in recent months.
The Spanish international was going to miss the game against Alaves anyway due to suspension.
Simeone, 47, led Atletico to a third-place finish in La Liga this season.
A 2-0 win over Malaga sealed the title for Zinedine Zidane's side.
Barca also without Javier Mascherano, Rafinha, Aleix Vidal and Jeremy Mathieu.
Barcelona must beat Eibar to have any chance of retaining the La Liga title.
Real will be crowned Spanish champions if they avoid defeat at La Rosaleda.
The Colombia international, linked with Manchester United, returned to training on Friday.
The Argentina international will miss Sunday's cash with Eibar with a thigh problem.
Real Madrid will lift their first title since 2012 if they get a point at La Rosaleda Stadium.