Department store operator Target Corp. and grocery chain Kroger Co. are in talks about a possible merger, tech focused magazine Fast Company reported on Friday, citing people with knowledge of the matter.

Neither companies was immediately available for comment.

However, a CNBC report, citing a source close to the matter, said there is "no truth" to the merger talks but the companies have had meetings over a Shipt partnership.

Shipt is a grocery delivery platform which Target acquired in late 2017.

The companies first started talks last summer about a partnership that could improve Target's grocery business and give Kroger customers more access to merchandise and e-commerce, the Fast Company report said.

While the talks started once again in 2018, the two companies appear to be struggling to decide whether a merger is the best path forward, the report said.

Shares of Kroger rose 4.6 percent in premarket trading on Friday while that of Target was trading up 2.2 percent.

Kroger has a market cap of $20.62 billion and Target $37.12 billion.