Goals from Neymar and Firmino ensured the Selecao reach the last eight stage of the championship.
But according to El Pais, Mbappe has not been on good terms with Neymar at club level.
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There had been suggestions that Real Madrid would try and bring Neymar to the Bernabeu but should Suarez arrive he is ready to affirm his commitment to PSG.
Mbappe's family have reportedly expressed their concerns to PSG as the forward is unhappy that he is being treated like a rookie by his senior teammates.
Neymar has endured a tough last few months with a bad injury ending his season early in Paris and a hard World Cup campaign ending in an exit at the quarter-finals stage.
Signing Coutinho would be primarily a move to keep Neymar happy, signing a player with whom he has been close friends for many years since the pair played together in Brazil's youth teams.
After also exiting the World Cup in the quarter-finals and missing much of the second half of the season through injury, Neymar himself needs a strong campaign to cement his status as a Ballon d'Or contender and Suarez could be the strike partner to help him achieve that. And in any case, PSG would first need to submit the offer with the club and not just the player's representation before any negotiations could commence.