Walgreens shares rose about 4 percent after the report.
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The acquisition would come amid a wave of consolidation in the health care sector. Among other proposals this year, Aetna offered about $37 billion for Humana, and Centene bid $6.3 billion for Health Net.
Many companies in the industry have looked to cut costs in recent years amid changes like the Affordable Care Act.
Walgreens had net sales of $76.4 billion in fiscal 2014, accounting for about 20 percent of the retail prescription drug market. Rite Aid had prescription drug sales of $18.1 billion in fiscal 2015, up from $17.2 billion in the previous year.
Shares of drugstore chain CVS also rose about 1 percent Tuesday after the report.
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Walgreens Boots Alliance declined to comment to CNBC. Rite Aid did not immediately respond to CNBC's request to comment.