The singer-and-actress - who has been romantically linked to the Smashing Pumpkins rocker since he helped her record the theme song, 'Who We Are', to her latest TV series 'The Price of Beauty' - says she and the musician have a special bond but refused to say whether the had or are dating.
She said: "I can't find good enough words to speak about Billy. He's a very, very dear friend. For him to give his time and his talents and share them with me, it was a great experience. And I hope we can do more music together."
Despite her troubled love life, Jessica - who has been in relationships with American footballer Tony Romo, womanising singer John Mayer and ex-husband Nick Lachey - is still willing to open up to new guys.
She added in an interview with Ryan Seacrest on his KIIS-FM radio show: "I'm not as guarded as you would think. I should probably be more guarded. I trust a lot of people, actually."
Jessica is also still angry with ex-boyfriend John for describing her as "sexual napalm" in an interview.
The 29-year-old star - who dated the 'Heartbreak Warfare' singer for nine months until May 2007 - said: "I still feel that with somebody that you have cared about for a long time you hope they can keep the intimate things intimate."