Office Depot Inc. and OfficeMax Inc. are discussing a merger with a deal possible this week, said a person familiar with the matter.

The companies have been discussing a potential stock swap that would create a single office-supply retailer to compete with Staples Inc., said the person, who asked not to be identified because the talks are private. Office Depot, the second-largest office-supplies retailer in the U.S., has been exploring options since September, when activist fund Starboard Value LP became its largest shareholder.