Sonoco signed a definitive agreement to acquire the firm for €286m ($383m) in August last year.
CMA referred the case for an in-depth phase 2 inquiry in January 2015 and panel members assessing the merger have provisionally decided to clear it.
When announcing the investigation in January, it said the merged company would be the largest manufacturer and supplier of composite cans for food products in the UK.
Sonoco told us in January it was 'disappointed' with the decision, considering approval in Germany and other countries.
Switch suppliers or packaging type
CMA believes customers of composite cans for food products will be protected from the risk of the merged company raising prices, or reducing quality, through their ability to switch to other suppliers or to alternative forms of packaging.
It is likely that if prices increased (or quality decreased) new firms would enter the market, potentially sponsored by larger customers looking for alternative suppliers, it added.
CMA said it has seen evidence this type of sponsored entry by a European supplier into the UK market would be likely.
Composite cans are rigid tubes with closures on each end and typical packaging uses include food products such as gravy granules, chocolate powder, crisps, crackers and coffee.
Both companies have UK subsidiaries with domestic production plants.
Martin Cave, inquiry chair, said the companies have been close competitors and main suppliers for many customers.
"After considering the available evidence overall, our provisional view is that, on balance, the merged company will be kept in check by most customers having the ability to switch to alternative suppliers or different types of packaging," he said.
"Already, trends in the consumer packaging industry have moved towards other types of packaging and many products which formerly used composite cans now use different formats.
"Larger customers also have the option of sponsoring new entry or self-supplying. As with all our provisional decisions, we will look closely at the responses we receive before we take a final decision."
February and January action
The CMA published an issues statement in February following its referral of the acquisition by Sonoco for a full phase 2 investigation in late January.
It was concerned a lessening of competition may result in higher prices or a reduction in choice or quality for customers.
The acquisition is expected to increase Sonoco's global consumer-related packaging and services business to $2.8bn in annual sales or 53% of the company's combined revenue of $5.3bn.
It is expected to increase net sales in Europe to 21% of total sales.
The inquiry group must publish its final report by 13 July. Anyone wishing to respond to the provisional findings should do so by no later than 5pm on 19 June.