Neymar says he is around a month away from completing his recovery from a foot injury, with Paris Saint-Germain also confirming his rehabilitation is on track.
Yet, despite PSG easing to the Ligue 1 and Coupe de la Ligue titles, with the chance of Coupe de France glory still to come, such domestic success is unlikely to be enough to save Unai Emery's job, with the Basque coach's expiring contract not expected to be renewed.
"We hope to have him in the team for some of our remaining matches".
Rony Lopes at least prevented PSG from claiming a clean sheet, though it was nothing more than a consolation and things only became more humiliating for Monaco, as Di Maria, a Radamel Falcao own goal and Julian Draxler's late strike in the second period capped a memorable night for the Parisians. They suffered a second leg defeat to Real Madrid which eliminated them from the Champions League, but have won six of the other seven games for which the Brazilian has been missing.
PSG are on course to win Ligue 1 but are unsure if the Brazil global will play again this season after breaking a bone in his foot.
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Kamil Glik's absence in the heart of the visiting defence was acutely felt as Lo Celso started the move that resulted in the opening goal on 14 minutes, sauntering into the box to tap in a Dani Alves cross.
Monaco pulled one back, Lopes latching on to Almamy Toure's cross from the right to score for the eighth consecutive time in Ligue 1 - a first in the French top flight since Shabani Nonda in 2003.
The hosts were gifted another when Falcao's attempt to clear a corner went horribly wrong, summing up Monaco's misery as the ball looped beyond Subasic on 77 minutes.
Brazil's first game is against Switzerland on June 17.
Earlier, Olympique de Marseille snatched a 3-2 comeback win at Troyes to stay fourth behind Lyon on goal difference.