The CMA says it is considering whether the transaction could "result in a substantial lessening of competition" within the market.
The Boards of OneSavings Bank and Charter Court Financial Services initially confirmed advanced merger talks in March.
Under the terms of their merger OSB shareholders would own approximately 55% and Charter Court shareholders 45% of the new group.
The firms also confirmed that Andy Golding and April Talintyre, currently CEO and CFO of OneSavings Bank, will retain their positions in the Combined Group.
The CMA is expected to announce its initial decision by the end of July.