Le10Sport are reporting that Newcastle have made an offer to sign the Brazilian on loan, with an option to make it a permanent deal next summer.
READ MORE: Newcastle set to complete Kenedy signing
The defensive midfielder impressed in Ligue 1 after a Â£12million move from Santos last summer.
Lille are understood to be keen on raising some money, but reports say that they have rejected Newcastle's move for the 21-year-old.
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However, they state that Lille have turned down the offer for the 21 year old Brazilian midfielder, preferring to sell him outright.
Maia was part of Brazil's 2016 Olympic gold-medal winning squad alongside the likes of Neymar and Gabriel Jesus.
Newcastle boss Rafa Benitez has already signed one midfielder this summer, Ki Yeung-sung on a free transfer from Swansea City.
Benitez is hopeful of completing a move for Brazilian winger Kenedy this week after agreeing terms with the Chelsea player.