The 19-year-old has developed into a star player for Les Rouge et Noirs and has already made 76 senior appearances for the club, registering four goals and five assists in 31 Ligue 1 games last season.
A number of Premier League teams including Arsenal, Manchester United and Tottenham Hotspur have been credited with an interest in Doue, but it is understood that both Paris Saint-Germain and Bayern Munich are making the most effort to win the race for the youngster's signature.
According to journalist Fabrizio Romano, Doue is taking his time to consider the projects presented to him by PSG and Bayern.
While PSG are said to be insistent that Doue would be 'ideal' summer signing, Bayern are readying an improved offer after seeing an opening bid in excess of €35m (£29.5m) rejected.
Doue, who is valued north of €60m (£50.5m) by Rennes and has two years left on his contact, is currently preparing to represent Thierry Henry's France at the 2024 Paris Olympics.
Dubravka set to leave Newcastle
Over in the Premier League, Newcastle United goalkeeper Martin Dubravka is reportedly set to leave the club this summer.
The 35-year-old has spent the last six seasons at St James' Park, keeping 46 clean sheets in 163 appearances across all competitions.
Dubravka benefitted from Nick Pope's long-term injury to make 30 appearances for the Magpies during the 2023-24 campaign, including 23 outings in the Premier League.
However, the return to fitness of Pope along with the arrivals of Odysseas Vlachodimos and John Ruddy means Dubravka is set to fall behind in the goalkeeping pecking order at Newcastle.
Dubravka has just a year left on his contract with the Magpies and Football Insider reports that the Slovakia international has been told he is free to find himself a new club.
The report adds that Dubravka is set to leave Newcastle in the 'coming weeks', although a move to Celtic - who have previously been linked with the shot-stopper - does not appear to be on the cards as they have already signed two goalkeepers this week in Kasper Schmeichel and Viljami Sinisalo.
Rasmus Kristensen completes Bundesliga loan move
Elsewhere, Eintracht Frankfurt have completed the loan signing of Leeds United right-back Rasmus Kristensen.
The 27-year-old joined Leeds for around £10m in the summer of 2022, but following the club's relegation from the Premier League, he made the loan move to Roma for the 2023-24 campaign and made 31 appearances in all competitions.
Roma opted against re-signing Kristensen and Frankfurt have since swooped in to recruit the Denmark international on a season-long loan deal with the option to buy for a reported £15m.
"Today is a great day for me. I'm delighted that I'm now at Eintracht Frankfurt," Kristensen told the club's official website. "I recently experienced the stadium in person at the European Championship and can't wait to play here soon."
Board member for sport Markus Krosche added: "We were interested in Rasmus as far back as three years ago and are delighted that it's now worked out. We had very good talks and sensed that he absolutely wanted to come to us. Rasmus is a robust, tough-tackling player, who's an out-and-out right-back but can also play at centre-back."
Kristensen has been handed the No.13 shirt and could be available to feature in Frankfurt's pre-season friendly match against Juarez on July 26.