Wal-Mart is understood to have consulted the Competition Commission over plans to buy the portfolio of 482 stores.
Reports suggest it hoped to get round any problem by launching a joint bid with Sainsbury. Other speculation focused on whether former Asda chief executive Allan Leighton was in the frame to front a Â£3bn takeover, funded by the Royal Bank of Scotland.
One analyst said: "There is no guarantee that the Competition Commission would let through a bid for Safeway from Wal-Mart. A joint bid would be an interesting way round the problem, but it would not be easy to do."
Safeway Communications director Kevin Hawkins said: "We said four weeks ago we have not received any approaches, we are not in talks with anyone. We want to remain independent, we've made it absolutely clear."
Allan Leighton was unavailable for comment.