Messi and Valverde have enjoyed a smooth relationship since the Spaniard became Barcelona boss back in the summer.
But Spanish website Don Balon claims that could be set to change, with the former Athletic Bilbao manager making a January transfer decision.
He supposedly is willing to let midfielder Denis Suarez depart, with the 23-year-old struggling for game time so far.
It is said Valverde is actually an admirer of the much-criticised Andre Gomes, who has toiled at ever since arriving from Valencia last summer.
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Big things were expected of the Portugal international when Luis Enrique splashed out £30million to secure his signature.
However, his impact at the Nou Camp has been minimal with reports also suggesting he had leaked information about Lionel Messi to Real Madrid's Cristiano Ronaldo.
Juventus, Tottenham and West Ham have all been tipped to end his miserable stint in Catalonia.
But Don Balon say Valverde now wants to offload Suarez instead.
Messi: Barcelona star is unhappy with Ernesto Valverde for his faith in Andre Gomes
Barcelona News: Ernesto Valverde wants to sell Denis Suarez
This has not sat well with Messi who wants the player to remain at the club.
He reportedly has a close relationship with the midfielder and, as a result, would rather Gomes be the one to leave.
Napoli could sign Suarez with the Serie A giants always on the eye out for creative talent.
And, should Valverde get his way, it is likely to damage his relationship with Messi.