Ed Miliband said he is not overly keen to see Rupert Murdoch launch a new Sunday tabloid to replace the axed News of the World.
"I wouldn't say I welcome it," he said when asked on Friday.
"I don't think they will be rushing to support me after my argument with News International."
Murdoch revealed plans to launch a new title in an email to his London staff on Friday ahead of a visit to The Sun's Wapping HQ.
Speaking on BBC Radio 5 Live, the Labour leader said that while Murdoch was entitled to open a new paper if he wanted, he should also leave "no stone unturned" to discover what happened at the company in the wake of the phone hacking scandal.
Five Sun journalists - including the deputy editor, picture editor and chief reporter - were held for questioning by Scotland Yard officers on Saturday on suspicion of making improper payments to police and other public officials. They have all been bailed.
Some journalists at the paper are said to be unhappy at the way they have been treated by senior management.
But Miliband said he was "outraged" that people would criticise the company for cooperating with the police investigating crimes.
"It would be quite wrong for them not to cooperate with the police," he said. "They should have been cooperating years ago with the police."