HLN reveals that an offer arrived from the French club, but did not meet Anderlecht’s €30m valuation.
Doku, 18, is one of Belgium’s most exciting talents and has already made two appearances for the national team.
In his second appearance for Roberto Martinez’s side, the speedy attacker scored against Iceland.
Anderlecht coach Vincent Kompany admitted recently that the club will “have to listen to all offer” for Doku.
But chief executive Karel Van Eetvelt previously stated that he wants €30m for Doku.
He pointed to Gent’s sale of Jonathan David to Lille for over €30m as the example they are following with Doku.
It remains to be seen if Rennes will make an improved offer for Doku, who has also been linked with Manchester City.
The feeling is that there could be a ‘quick agreement’ if Rennes offer Anderlecht’s asking price for the teenager.
Doku has started the new season strongly with two goals and four assists for Kompany’s side.