AMSTERDAM—John Malone is on the hunt for another trophy property to add to his global cable and telecommunications empire.

Liberty Global Inc., the media mogul's international cable holding company, owns 28.5% of Dutch cable and telephone company Ziggo NV and in August made an offer for the rest of it. Ziggo in October said it had rejected the offer. But the company said Thursday that it is in talks with Liberty Global about a potential takeover that analysts said could value the company at €7 billion ($9.65 billion).

The two sides continued to talk despite the rejection, a person familiar with the situation said, adding that Liberty originally hoped to strike a deal in the first quarter of next year. Although an agreement this year seems unlikely, Liberty might speed up its efforts to reach an agreement with Ziggo's management after Thursday's announcement, the person said.

A spokesman for Liberty Global declined to comment.

U.S.-based Liberty Global has been an active deal maker this year, acquiring U.K. cable-television and Internet provider Virgin Media for $16 billion and raising its stake in Telenet Group Holding NV of Belgium.