The owner of the New York Stock Exchange has made a takeover offer for eBay Inc. that could value the sprawling online marketplace at more than $30 billion, according to people familiar with the matter.

Intercontinental Exchange Inc., known as ICE, has approached eBay in the past and did so again recently, the people said. The companies aren’t currently in formal talks, and there is no guarantee eBay would agree to a deal.

Should...