Blanc is under pressure due to PSG's stuttering title defence and his side were very unconvincing in their 2-1 win on Wednesday.
Early goals from Edinson Cavani and Javier Pastore ensured they did enough to reach the last 16 despite a late scare.
Diego Rolan pulled a goal back for Bordeaux in the second half before PSG defender Zoumana Camara was sent off with seven minutes to go.
Blanc left Sweden star Ibrahimovic on the bench for the duration of the match and said afterwards that he wanted to avoid an unnecessary suspension.
"I wanted to rotate the squad," Blanc said.
"What is more, he has accrued two yellow cards and a third one would have seen him suspended.
"Also he needs some rest so he is on top form for the weeks ahead and I am optimistic he will be.
"We have a loaded schedule in February, including the Champions League last-16 clash [against Barcelona]."
PSG sit third in Ligue 1, four points adrift of leaders Lyon.
