Apple launched its own mapping service in early September, replacing popular Google Maps, which previously came pre-loaded in Apple devices, but the service contained embarrassing errors and drew fierce criticism.
Google's mapping tool has since returned to the iPhone, after user complaints, a public apology from Apple's CEO and the firing of a top executive.
Apple's negotiations with New York-based Foursquare come as the tech giant has been talking to a number of companies that collect local data to improve its new mapping product, the paper said.
The move is also latest sign of Apple's plans to build more local data and tightly integrate local services into the iPhone and iPad so as to compete with Google Inc.
Apple could not immediately be reached for comment by Reuters outside of regular U.S. business hours.
© Thomson Reuters 2012