Is Liberty Media (NSDQ: LINTA) once again interested in purchasing part of AOL? In an interview with CNBC this morning (via Tech Trader Daily), Liberty Media CEO Greg Maffei (pictured) was asked whether it was “just a nonsense rumor” that his company had an interest in Time Warner’s internet business. His response: “There are assets inside Time Warner (NYSE: TWX) including AOL that we’d certainly like to talk to Time Warner about, and we have ongoing positive discussions. Whether those lead anywhere, we’ll see.”

Last fall, Liberty said it was in “limited talks” to purchase AOL’s dial-up business in exchange for some of its holdings in Time Warner, although Time Warner’s board decided late last month to spin off AOL, with the access business intact. Liberty owns about three percent of Time Warner.

Other highlights from the interview:

—DirectTV:  DirectTV CEO Chase Carey left for News Corp (NYSE: NWS) earlier this month. Asked whether he was interested in now taking on that role, Maffei would not comment. He also talked up DirecTV’s prospects—saying that subscription for paid TV services continued to rise even as the advertising market had dropped.

—Tracking stocks: Liberty is famous for its use of tracking stocks, but Maffei said that “I think a lot of our stocks will eventually become asset based.”

• It’s Official: Carey To Leave DirecTV, Succeed Chernin At News Corp.
• Liberty’s Malone: We’ve Held Limited Talks To Get AOL Access
• Time Warner Board Approves AOL Spinoff; Dial-Up Business To Remain With AOL