A deadline for the two companies to announce their intentions by today has been extended to May 19, the pair said in a statement.
Details of the possible merger between electrical retailer Dixons, owner of PC World and Currys, and mobile phone retail giant Carphone Warehouse were revealed last month, sending shares in both companies soaring.
But both stocks fell today as it transpired that the initial deadline of 5pm today would not be met. Carphone Warehouse is valued at about £1.9 billion and Dixons at £1.8 billion.
The high street retailers said that the announcement of talks on February 24 was made "when discussions were at a very preliminary stage".
It added: "Both parties have agreed that they require more time to evaluate a potential merger of the two businesses."
The statement said that an extension had been granted by the Takeover Panel. It said discussions were ongoing but there was no certainty a firm offer would be made.
Between them, the two companies have more than 3,000 stores with annual sales of more than £12 billion.
Dixons, founded in the 1930s and based in Hemel Hempstead, Hertfordshire, is one of the largest consumer electronics retailers in Europe, employing more than 31,000 people in 12 countries.
Carphone Warehouse was founded in 1989 by Sir Charles Dunstone, who still owns 23% of the company.
Both companies have weathered the difficult trading conditions in UK retail, with Dixons recently reporting its second year in a row of improved Christmas trading as it benefits from the demise of rival Comet.
Carphone recently said like-for-like revenues rose 5% in the UK during the quarter to December 28 as its performance was boosted by the popularity of more expensive smartphones.
Sir Charles is reportedly in line to become chairman of the newly-merged company with the chief executive's role to be taken by Dixons boss Sebastian James.
However, the companies still need to agree how the tie-up would work, according to the Sunday Telegraph, with Sir Charles said to be insisting that it is a "merger of equals".