The deal is conditional on the disposal of 42 pubs, which the CMA says would address concerns the combined company would face limited competition in 51 areas.
The watchdog says the sale would provide an 'effective resolution' to fears a monopoly could lead to higher prices and lower quality products for customers in certain locations.
Stonegate is seeking to acquire Ei for c.£1.3m.
If approved the merger will create the UK’s largest pub group with almost 5,000 sites, including Stonegate’s Slug & Lettuce and Walkabout chains.
The CMA says it has ‘reasonable grounds for believing’ that the proposals will be acceptable and has until 19 February to formally decide whether to approve the tie-up.
The watchdog has the power to block deals if it believes consumers will have less choice.
It launched a formal investigation in to Amazon’s investment in restaurant delivery platform Deliveroo in December.