Ahold and Delhaize have substantial operations in their respective home countries of the Netherlands and Belgium, as well as in the U.S. The market capitalization of the former is around 16.4 billion euros ($18.3 billion), while Delhaize's is roughly 8.6 billion euros.
Speculation about a merger of the two supermarket chains dates back to at least 2006, but shares in each companies rocketed Monday after new rumors appeared in the Belgium and Dutch media over the weekend. Ahold shares rose around 18 percent on Monday and Delhaize shares jumped 15 percent.
Flemish newspaper De Tijd reported on Saturday that the retailers had held merger talks "at the highest level," citing "multiple sources."
Both Ahold and Delhaize declined to comment on the rumors.
The merger could create savings of roughly 1 billion euros, the Netherlands' Rabobank said. Patrick Roquas, senior equity analyst at the bank, told CNBC that they would be split around 50:50 between revenues and purchasing synergies.
"The sector is suffering from eroding margins… and a combination of both companies could really solve that issue," he added.
However, Bruno Monteyne, senior analyst at Sanford C. Bernstein, panned the prospective deal, saying that savings would be limited as the two retailers were "neighboring" chains rather than rivals.
"I think there's very little merit in the deal in the past and today. Large food retailers rarely ever do successful mergers. In this case of Delhaize and Ahold it is probably the worst kind of combination," Monteyne told CNBC on Monday.
The chains were "neighboring" rather than "overlapping" retailers, he said.
"The thing is that Ahold and Delhaize are not really rivals in the same neighborhood. Belgium and the Netherlands may be next door to each other, but they have very limited overlap. It's the same in the U.S.," Monteyne added.
Ahold shares have more than doubled since 2011-lows of less than 8 euros per share, to around 18.33 euros on Monday, making the company nearly twice the size of Delhaize. This means that a tie-up is more likely to be an acquisition than the merger of equals first touted in 2006.