The CMA said it was not accusing Google of anti-competitive practices at this time, but it has set out a "roadmap" of changes the company could make to its business ahead of a final decision in October.
These could include requiring "choice" screens for users to access different search providers as well as more transparency and control for publishers whose content appears in search results.
The watchdog said the average person in the UK makes between five and 10 searches a day and businesses spend an average £33,000 a year on Google adverts, but if competition was working well the figure could be lower.
"Google search has delivered tremendous benefits but our investigation so far suggests there are ways to make these markets more open, competitive and innovative," said CMA chief executive Sarah Cardell.
She said that proposed "targeted and proportionate" changes "would give UK businesses and consumers more choice and control over how they interact with Google's search services".
But Google said that the outcome of the investigation and the suggested changes "could have significant implications for businesses and consumers in the UK".
"The CMA has today reiterated that 'strategic market status' does not imply that anti-competitive behaviour has taken place - yet this announcement presents clear challenges to our business in the UK," a spokesperson said.
They added the UK has "historically benefitted from early access" to Google innovations but said this could change as a result of "punitive regulations".