The La Liga champions are pushing to re-sign the PSG forward before the Spanish transfer window closes on September 2.
Real Madrid are also exploring the possibility of acquiring Neymar, who is desperate to depart the Parc des Princes.
Barcelona are the first to make a formal bid for the Brazilian, but PSG are demanding more cash and more players in return.
It is thought that the French giants would give serious consideration to an offer of £93m plus Coutinho, Ivan Rakitic and Nelson Semedo.
However, although Barcelona are open to losing Rakitic this summer, they want to keep hold of Semedo.
Madrid, meanwhile, will first have to sell players to raise funds for their pursuit of Neymar.
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