Shares in both companies surged in premarket trading Friday after Fast Company reported the two were discussing a merger deal. It cited several people with knowledge of the matter.
The report said the two companies first started discussing a partnership last summer but decided "a merger is the best path forward."
Target shares were up fractionally in Friday after jumping during the premarket when the report was published. Kroger's stock rose 8 percent initially on the report, but later pared much their gains.
The two have had meetings over a Shipt partnership, CNBC's source said. Target acquired same-day delivery company Shipt for $550 million in cash in December, in a move to bolster its supply chain and compete with rivals on speed.
Target has notably struggled in the fresh food category relative to its peers. Its supply chain for those items has lagged, people familiar with the situation have told CNBC, opening the door for potential partners such as Kroger to bring expertise in the area.
Just last year, Target tapped a former Kroger exec, Jeff Burt, to head its grocery department. Since then, the company has made incremental changes to its food offering, redesigning that area of the store as part of a bigger remodeling strategy. But analysts and investors continue to call out the business as lackluster.
"We believe Target has much further to go before the grocery business is fully fixed," GlobalData Retail Managing Director Neil Saunders said.
Instead, Target has focused on its private-label brands for apparel and home goods of late, beefing up those categories before moving into food, which can be more capital intensive and the return on investment isn't as compelling.
Kroger and Target did not respond to CNBC requests for comment.