As Microsoft Corp. explores the possibility of making another move for Yahoo Inc., the Internet company continues to flirt with other potential partners.

Yahoo has picked up discussions with Time Warner Inc. over a combination, say people familiar with the situation. The renewed talks come after a lull following Microsoft’s withdrawal in May of its $47.5 billion offer to buy Yahoo. Still, the talks aren’t as serious as they were in April, when a combination valued Time Warner’s AOL unit at about $10 billion. Yahoo’s stock has since declined sharply.