The Brazil international wants to swap Ligue 1 for La Liga before the Spanish transfer window closes on September 2.
PSG also want to sell a player they paid a world-record £198m for in summer 2017, but only if the price is right.
Barcelona and Real Madrid are both keeping tabs on the situation, with Neymar favouring a return to the Camp Nou over a move to the Bernabeu.
Nevertheless, Barça are yet to submit a satisfactory offer to PSG, who were left unimpressed by their cash-plus-Philippe Coutinho proposal.
And that could allow Madrid to jump to the front of the queue, although they will first need to sell at least two first-teamers to raise the necessary funds.
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