The United States striker has struggled to break into the Ligue 1 side's squad and is making the move in order to get more minutes.
According to reports in France, the young forward will arrive in Dubai this evening, with his lawyer in tow, in order to join in with the Scottish champions' warm-weather training camp.
The 18-year-old has only appeared twice for the defending Ligue 1 champions, but bagged his first goal for the club in August.
Celtic are without Leigh Griffiths, who is taken a leave of absence to deal with mental health issues, so they have boosted their attacking power with the young striker.
The Hoops are only separated from their fierce rivals by goal difference after Rangers got their season off to a flying start under new boss Steven Gerrard.
Yesterday, Gerrard confirmed that his former England team-mate Jermain Defoe was joining his side on a loan deal.
So the young addition up front will surely be welcome news to Celtic fans.
Should the son of Ballon d'Or winner George Weah impress during his spell at Celtric Park, he could well extend his stay for another season.
But, if he struggles to adapt to life in the Scottish Premiership then PSG are open to the idea of loaning him out to a fellow Ligue 1 side to continue his development.
Weah has broken into his national side's senior squad and has appeared alongside new Chelsea signing Christian Pulisic.
The young forward scored his first senior goal against Bolivia in May.
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