Thauvin, who completed a transfer to Marseille from Lille on September 2, has not played a club game this season and while the 20-year-old Orleans-born playmaker is expected to feature in Marseille's match away to Toulouse, Baup does not believe he is ready to start.
Although Thauvin started all seven matches for France at the FIFA U20 World Cup in Turkey as the French won the title, Baup is convinced the former Bastia youngster lacks fitness.
"I don't know (if Thauvin will start)," Baup said on Thursday.
"I haven't taken the decision.
"Last week, he was in full training.
"He played one hour in a friendly against Istres. He trained this week (but) even with his training, I am not sure he can play 90 minutes.
"Whether he will start or not, I still have to think about it."
Despite Thauvin's lack of fitness, Baup wants to include the attacking midfielder in his travelling party for the trip to Toulouse.
"He is late in terms of preparation, that's obvious," Baup said.
"But I think he can and will take part in the game."
Marseille head into Saturday's match with nine points from four rounds and sit second in Ligue 1, while Toulouse are bottom of the table with just two points.
But Baup remains wary of Toulouse and believes the club that finished 10th in the French top flight last season will improve.
"Things are falling into place (for Toulouse)," Baup said.
"They're a very good team who didn't get the results they deserved, not because of their new tactics but because they recruited players from different countries.
"They are very strong and they will do better.
"But hopefully, that will happen later on; not against us."
