A 2-0 loss at home to Atalanta continued a dismal run for Bologna that has seen them win just twice in 2014.
Ballardini's side are just two points clear of the relegation zone in the Serie A, and their form led to protests at their Stadio Renate Dall'Ara home on Saturday.
Pioli was sacked by Bologna in January, but reports suggest he could be back to replace Ballardini for Saturday's trip to Inter.
"I don't know anything about that," Ballardini told Sky Sport Italia.
"Do I feel the club has faith in me? Yes.
"We take the jeers, as people who go to the stadium have every right to express their dissatisfaction.
"I was very disappointed by our performance on Wednesday against Chievo, but it was a good game today."
The win was Atalanta's sixth straight and came on the back of first-half goals from Giuseppe De Luca and Marcelo Estigarribia.
Despite the loss to a team sitting seventh, Ballardini praised his players and said he could ask for no more from them.
"The team did what it had to against a side in good shape that notched up a sixth straight win," Ballardini said.
"I cannot ask for more from my players, as they gave it everything they had and we simply couldn't finish off our chances.
"Don't forget as things stand right now we are not in the relegation zone. We'll see what happens tomorrow. The team wants to get out of this situation and we will do it."
