The Competition Commission said Rank's deal to buy 23 casinos could reduce competition in Aberdeen, Liverpool, Stockton-on-Tees, Bristol and Cardiff, as well as in Edinburgh, where it has the licence to develop a new casino.
The planned acquisition of the 23 sites by the Mecca Bingo owner would see it leapfrog Malaysian firm Genting as the UK's biggest player, giving Rank's Grosvenor casino arm 57 sites.
The Commission fears the loss of one of the UK's three major casino operators could mean customers in several areas may lose out.
Inquiry chairman Martin Cave said: "We have found that casinos vary their offer in response to local competitive conditions and while there is limited scope to compete on price, casinos try to attract customers through customer service, promotions, events and the range of games available."
The Commission will publish its final report on February 20, when its other sanctions could include blocking the whole deal altogether.
Rank said in October that discussions were ongoing over changes to the previously agreed terms of the £205 million deal, following the referral to the Competition Commission by the Office of Fair Trading.
The majority of Rank's casinos are outside London, with the company focused on the faster roll-out of its G Casino format, which attracts a younger, less formal crowd.
The Rank business employs more than 3500 staff.
Rank is listed on the London Stock Exchange but is majority owned by Guoco, the investment vehicle of Malaysian billionaire Quek Leng Chan.