Casey's General Stores, under pressure from activist investor JCP Investment Management, has submitted an initial bid for Kroger's roughly $2 billion convenience-store business, sources familiar with the situation tell CNBC.

JCP Investment Management in January called for the Ankeny, Iowa-based convenience store operator to explore strategic alternatives, including a potential sale. Buying Kroger's convenience-store business could stave off pressure to sell, sources say. Casey's in 2010 successfully fended off a hostile bid from larger peer Alimentation Couche-Tard.

JCP, along with BLR Partners and Joshua Schechter, collectively own $45 million of Casey's common stock, as of Jan. 3. Casey's has a market capitalization of $4.6 billion.

Kroger announced in October it was exploring strategic alternatives for its more than 780 convenience stores, which operate under names such as Kwik Shop, Turkey Hill and Tom Thumb. It said it is working with Goldman Sachs on the potential sale.

Casey's, which is working with an investment bank, is one of several parties looking to buy the stores and may not ultimately be the victor. Final offers in the sale process are due in early February, the sources said.

The sources requested anonymity because the information is confidential. Casey's declined to comment.

Casey's has been a relatively quiet acquirer when compared with its peers that have driven the consolidation of a still-fragmented industry. Last year, Canada's Couche-Tard bought CST Brands for roughly $4.4 billion. Earlier this month, 7-Eleven parent Seven & i Holdings completed its roughly $3.3 billion acquisition of 1,030 stores from Sunoco.

Still, Casey's CEO Terry Handley recently told analysts it would "further augment unit growth with acquisition opportunities."