A source close to the transfer has told Sky Sports that a deal could be done for around £8million and there is a great deal of interest.
European heavyweights Barcelona and AC Milan are believed to be amongst a host of clubs keeping tabs on Sakho's situation.
Liverpool have been strongly linked in recent weeks, but it is understood Arsenal, Tottenham and Manchester City are also keen.
The France international has come through the youth ranks at the Parc des Princes but he has just 12 months left on his current deal.
PSG want the 23-year-old to stay but, with big-money buys Thiago Silva, Alex and, most recently, Marquinhos in the squad, the club are considering letting Sakho leave now rather than losing him for nothing next summer.
The source told Sky Sports: "PSG are ready to do a deal, and the interest is big - he is a top talent, and it is not surprising.
"He is a top player and, although PSG are willing to sell, they do still want good money for him, but there is now a good chance that he will move and he could very well be heading for England."
PSG boss Laurent Blanc remains keen for Sakho to stay, despite the fact he has said he wants to leave.
"When players express their desire to leave in their head, it is not always clear," Blanc said.
"He expressed his desire to the club. Will there be a solution by September 2nd? I hope so, for the player and for the club."