The Smashing Pumpkins frontman is believed to have grown uncomfortable with the amount of attention their romance has attracted since reports first linked the pair last month.
However, Corgan reportedly insisted that the couple remain on good terms and that he still intends to assist the singer with her forthcoming album.
An insider told the New York Daily News: "Dating Jessica publicly can be intense. Billy maintains a quiet, private music-focused life and the taste of publicity he got while being with Jessica was an eye-opener.
"Billy likes Jessica, but he will work to keep their relationship as it is and focus on the music. They are not getting serious, but Jessica has had so much fun with him."
The source added: "She once was a slave to what people thought and said about her, and her time with Billy has brought out an even more mature and toned-down Jessica."