"They are getting to know each other," says the source. "He's a nice guy."
On Friday, Simpson, 29, and Corgan, 42, were spotted together in New York City. She was in town earlier in the week for sister Ashlee Simpson Wentz's Broadway debut in the musical Chicago.
Corgan's spirituality may just be what appeals to Simpson. On Sept. 11, Simpson, who has often spoken about how important God is to her and whose father, Joe Simpson, is a former pastor, Tweeted: "My friend, Billy Corgan, has a pure and enlightening outlook on faith."
No matter where this new romance heads, a friend of Simpson's says she is happy that she is dating again – especially after Dallas Cowboys quarterback Tony Romo broke up with her the night before her 29th birthday this summer.
"She's a great girl," says her friend. "She's really sweet. She's had a tough year. She deserves the best."