A source said: "They are getting to know each other. He's a nice guy."
Meanwhile, Jessica's twitter postings have revealed she has been building up a close relationship with Billy over the last few months.
On September 11, Jessica tweeted: "My friend, Billy Corgan, has a pure and enlightened outlook on faith."
Jessica - who, at 29, is 13 years younger than Billy - was pictured leaving New York's Ritz Carlton Hotel with Billy last week.
The pair were first romantically linked in November when they both attended a party in Los Angeles.
A source said: "She has completely fallen for Billy and his easygoing, smart attitude. She says she wants to take things a lot further.
"She had secretly been crushing on him for months and felt there was a connection at the party.
"As the night went on things got more intense and they talked with their faces just inches apart."
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