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The 29-year-old is said to have "fallen hard and is smitten" with the Smashing Pumpkins singer, 42, after the pair started "officially dating" several months ago.
However, the news is not thought to have been welcomed by Simpson's friends. A source told E! Online: "They think he's too old for her. No-one takes any of her boyfriends seriously anymore because she has had so many. They're sick of all of them being 'The One'."
The two were first romantically linked in November after they were seen at a party in Los Angeles.
The insider added: "She has completely fallen for Billy and his easy-going, 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."
In September, Simpson wrote on her Twitter: "My friend, Billy Corgan, has a pure and enlightening outlook on faith. Go to his new website!"
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