The German has been a bit-part player at PSG over the last two years and the Parisians are more than keen to sell him in the final weeks of the transfer window.
Draxler has also been linked with a move to England, with Leeds and Arsenal both credited with holding an interest in the German.
But the midfielder is in no mood to leave PSG and the Parisian lifestyle, and is willing to see out the final year of his contract at the Parc des Princes.
Lazio are now willing to try their luck with Draxler and, according to Italian outlet Tutto Mercato, they are prepared to offer a five-year deal to the player.
The Serie A giants have money left from their failed moved to sign David Silva and are prepared to reallocate the budget towards the Germany midfielder.
Lazio coach Simone Inzaghi wants to add more creativity to his squad and has asked the club to bring in a creative midfielder,
The Serie A giants want to bet on Draxler but they are only likely to move once they manage to sell Felipe Caicedo.