The newspaper cited people familiar with the matter who were not named.
Atlanta-based Intercontinental Exchange, better known as ICE, declined to comment on the report. EBay did not immediately respond to request for comment.
Activist shareholders have been pushing eBay to make some significant strategic changes, including selling off its ownership of online ticket resale site StubHub.
Shares in eBay, which is based in San Jose, California, closed Tuesday up almost 9%. ICE's shares slumped more than 7%.
This story has been updated to correct the name of ICE. It's Intercontinental Exchange, not International Exchange.