Monaco missed the chance to return to the top four after Benjamin Moukandjo scored a late equaliser for Reims.
Paris Saint-Germain brushed aside Bordeaux 3-0 in Ligue 1 on Saturday, while Monaco won 3-1 at Bastia.
Two goals in the final 12 minutes lifted Monaco to a 3-1 victory at Bastia which moved them up to sixth in Ligue 1.
Monaco and Benfica played out a goalless Champions League Group C draw at the Stade Louis II on Wednesday.
Stuttgart concede that keeping Antonio Rudiger will be a struggle, but only intend to do business with a 'big outfit'.
Fabian Lemoine earned Saint-Etienne victory at Lorient in Ligue 1 on Saturday, while Nantes were held by Reims.
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