The Russian champions have held talks about acquiring 27-year-old Draxler, who PSG are reportedly open to selling.
But their efforts, described as ‘intensive’, appear to be in vain with Draxler continuing to insist on a Paris stay.
The former Schalke star is out of contract next June and can negotiate a move to another club from January.
A World Cup winner with Germany, Draxler joined PSG from Wolfsburg three years ago for a sum of €42m.
Although he was in the starting eleven for just seven Ligue 1 games last season, Draxler has started PSG’s last two games against Metz and Nice.