There has been a host of speculation surrounding the Frenchman's future this summer, with a number of Premier League clubs believed to have been interested in his services.
However, according to journalist Ben Jacobs, PSG have won the race for the attacker, who is now set to undergo a medical with Luis Enrique's side ahead of signing a long-term deal.
The transfer package is allegedly worth €60m (£51.3m), including add-ons, and PSG were able to convince Doue to move to the club during a meeting after the Olympics, where Doue was in action for his country.
The 19-year-old has represented Rennes on 63 occasions over the last two seasons, boasting a record of eight goals and seven assists, while his Ligue 1 record stands at seven goals and six assists in 57 appearances.
Leicester 'leading the race' for Skipp
Meanwhile, Leicester City are reportedly at the head of the queue for Oliver Skipp, who is set to leave Tottenham Hotspur before the transfer window closes for business.
Ipswich Town have been heavily linked with Skipp in recent days, but according to Football Insider, it is another promoted club that lead the race, with Leicester in a strong position to sign the midfielder over the next couple of weeks.
The 23-year-old is allegedly viewed by the Foxes as the ideal replacement for Kiernan Dewsbury-Hall, who made the switch to Chelsea earlier this summer.
Skipp, who has another three years left to run on his Tottenham contract, has represented his North London club on 106 occasions, scoring once and providing two assists.
Last season, the Englishman made 24 appearances for Ange Postecoglou's side, including 21 outings in England's top flight, but Spurs are open to letting him leave before the transfer window closes for business.
Villa 'working on a deal' for Mosquera
Elsewhere, Aston Villa are allegedly working on a move for teenage centre-back Yeimar Mosquera.
The 19-year-old plays his club football for Colombian side Orsomarso SC, and it is understood that a number of European teams are keen on his signature.
According to The Athletic, Villa have been in touch with second-tier outfit Orsomarso and are confident of completing a deal before the transfer window closes.
Mosquera, who has been capped at Under-20s level by Colombia, has scored twice in 20 appearances for his current team in all competitions.
Villa have been active during this summer's transfer window, with their biggest signing in terms of a fee proving to be Amadou Onana from Everton.
Meanwhile, Ian Maatsen, Cameron Archer, Jaden Philogene, Samuel Iling-Junior, Lewis Dobbin, Enzo Barrenechea and Ross Barkley have also moved to Villa Park in the current market.