Deal-of-the-day website LivingSocial Inc., which has courted bargain-hunting consumers for the past few years, is now looking to win over public investors.

LivingSocial, which competes with larger rival Groupon Inc., is seeking to raise about $1 billion from an initial public offering, valuing the Web firm at between $10 billion and $15 billion, people familiar with the matter said.

The...