Known as Project X, the Sun on Sunday has been widely rumoured to be in the works for some months, including recent reports suggesting that late April had been earmarked for its launch.
However, the Financial Times cites three senior insiders at publisher News International as saying that the project has been halted after raids by police on four senior journalists at the weekend.
The men were named by colleagues as Graham Dudman, a former managing editor of The Sun, and Fergus Shanahan, a former deputy editor, along with the paper's current head of news Chris Pharo and the serving crime editor Mike Sullivan.
They were all questioned by police on suspicion of corruption under the 1906 Prevention of Corruption Act, as well as aiding and abetting misconduct in a public office.
A serving police officer was also arrested at the weekend, and all five men were bailed until April and May.
The Financial Times said that News International is concerned that the negative publicity surrounding the arrests would damage the launch of the Sun on Sunday.
The paper would get the publisher back into the lucrative Sunday market following the decision to scuttle the News of the World at the height of the phone hacking affair.
But one source said: "It has gone way on to the back burner since Saturday."
Neville Thurlbeck, the former chief reporter of the News of the World, has even claimed: "The launch of that newspaper is not even being discussed now."
News International declined to comment on the report.