Amazon should acquire Rite Aid to obtain state pharmacy licenses and add a regulatory-cleared infrastructure, according to one Wall Street analyst on Tuesday.

If Amazon were to launch pharmacies in Whole Foods, on Prime and Prime Now, an acquisition of Rite Aid would accelerate market share gains, according to Cowen analyst John Blackledge.

Both Amazon and Rite Aid offered no comment for this story. Shares of Rite Aid were up more than 5 percent late morning Tuesday after the Cowen report.

The deal suggestion was part of a larger report by Blackledge on why Amazon should get into the business of selling prescription drugs. The e-commerce giant has been quietly exploring ways to expand into the health-care industry. CNBC reported in May that Amazon has been recruiting health insurance experts to develop an internal pharmacy benefits manager for Amazon employees.

"Our Cowen proprietary survey data suggests 67 percent of Amazon Prime members would purchase prescription drugs through Amazon if they were available," wrote Blackledge. "Depending on the pace Amazon would seek to enter the market, an acquisition such as Rite Aid could accelerate the pace and be a relatively low-risk acquisition given that it currently trades at an enterprise value of only about $5 billion."

If an Amazon-Rite Aid deal were to materialize, the analyst argues that Amazon's U.S. retail pharmacy business could generate about $20 billion in 2019 with 10 percent market share. Amazon would inherit pharmacy licenses in 19 states as well as adopt six distribution centers and 2,575 regulatory-cleared stores, a sizable leg up for the e-commerce giant.

Many Wall Street strategists view the recent CVS-Aetna merger talks as evidence that some of the industry's major players are also wary of Amazon's ambitions in the space. If Amazon entered the pharmacy benefit manager space, Amazon could serve as its own mail-order drug business.

"We think Amazon could enter the pharmacy benefit manager business (PBM)," added Blackledge. "A simple case one can make for Amazon to enter the PBM space is that it can serve as its own mail pharmacy, and capitalize on Prime 2-day delivery. From there, Amazon could build out its own retail network, and find itself working with other retail pharmacy chains to participate in its retail network."

Earlier this year drugstore chain Walgreens Boots Alliance ditched its deal to buy Rite Aid after struggling to win antitrust approval.

Instead, Walgreens received clearance from the Federal Trade Commission to buy 1,932 stores from Rite Aid for $4.38 billion.