The boom in uptake has prompted scrutiny from regulators who have questioned whether customers are being pushed to sign up to schemes.
The CMA kicked off an investigation into loyalty programmes earlier this year.
At the time, it raised questions over whether customers not signed up to loyalty card schemes were paying more than they should be.
The CMA said, as part of its review, it would be assessing whether supermarkets were artificially inflating prices for regular shoppers to benefit loyalty card customers.
Consumer rights group Which? last year accused supermarkets of engaging in “dodgy tactics” to try to push shoppers onto schemes.
It claimed both Sainsbury’s and Tesco had raised prices of products in the run-up to launching a loyalty card promotion to create the illusion that shoppers are getting better value.
Both supermarkets refuted the claims, saying prices were rising across the board because of inflation.
In an update to Friday’s market review, the CMA said early analysis suggested it was “unlikely to identify widespread evidence of loyalty promotions that mislead shoppers in this way”.
The watchdog said it had been gathering information from grocery retailers that offer loyalty pricing and was assessing what happens to prices before, during, and after a product goes onto a loyalty price promotion.
It is also comparing a sample of supermarkets’ loyalty prices to those prices charged by rivals at the same time. The CMA’s next update is expected in November.