The relationship between Barcelona and Dembele broke down after the winger continuously refused to sign a new contract despite multiple offers.
He will be out of contract in the summer and Barcelona have made it clear that they will like him to leave before the window slams shut tonight; he has been linked with several clubs, including Manchester United, who are claimed to have made a late enquiry.
PSG have been in talks with his representatives and there are claims that an agreement over a contract is in place between the two sides.
But according to French daily Le Parisien, PSG will not be signing the winger before the transfer window closes tonight.
PSG do not have any financial latitude to bring in new signings due to the bloated nature of their squad.
The Parisians are not likely to sell any player to make way for any new signing before the window closes tonight.
Barcelona also want €20m in a transfer fee for a player who will be available on a free transfer in the summer.
It remains to be seen if Manchester United make a late offer to Barcelona and attempt to convince the player.