The Competition and Markets Authority (CMA) said that investigations have raised "local competition concerns in relation to the supply of road fuel in 36 areas across the UK".
EG Group, the forecourt giant owned by Mohsin and Zuber Issa, operates 395 petrol stations, while Asda owns 323 sites.
Joel Bamford, senior director of mergers at the CMA, said: "Our job is to protect consumers by making sure there continues to be strong competition between petrol stations, which leads to lower prices at the pump.
"These are two key players in the market, and it's important that we thoroughly analyse the deal to make sure that people don't end up paying over the odds.
"Right now, we're concerned the merger could lead to higher prices for motorists in certain parts of the UK.
"However, if the companies can provide a clear-cut solution to address our concerns, we won't carry out an in-depth Phase 2 investigation."
A spokesperson for the Issa brothers and TDR Capital: “We will be working constructively with the CMA over the course of the next 10 days in order to arrive at a satisfactory outcome for all parties within Phase 1.
"This would provide welcome certainty for our colleagues, suppliers and customers, and allow us to move forward with our exciting plans for investment and growth at Asda.”
Support The Yorkshire Post and become a subscriber today.
Your subscription will help us to continue to bring quality news to the people of Yorkshire. In return, you'll see fewer ads on site, get free access to our app and receive exclusive members-only offers.
So, please - if you can - pay for our work. Just £5 per month is the starting point. If you think that which we are trying to achieve is worth more, you can pay us what you think we are worth. By doing so, you will be investing in something that is becoming increasingly rare. Independent journalism that cares less about right and left and more about right and wrong. Journalism you can trust.