The former Labour leader said any bid must be wrong when judged by the same standards as Mr Murdoch’s previous attempt to take full control, which was derailed amid the fallout from the phone-hacking scandal.
Culture Secretary Karen Bradley told MPs she would have 10 days to refer the bid to Ofcom once she had formal notification, which she has not yet received.
But Mr Miliband said it would be “totally and utterly unacceptable” were the deal to be approved over the parliamentary recess, with MPs having their last day in the Commons on Tuesday and not due to return until January 9.
Asking an urgent question on the issue, Mr Miliband said: “This bid shows the Murdochs have learnt nothing and think they can get away with everything.
“If it was wrong for the Murdochs to own 100% of Sky in 2011 and 2012, it is wrong today.”
He added: “Can she hear the message loud and clear, that if this House were to return on January 9 to find the waving through of this bid, it would be totally and utterly unacceptable, and fly in the face of the expressed will of this House and the country.”
Mr Miliband told the Commons that back in 2011, MPs unanimously urged the withdrawal of the bid for Sky, and in 2012 Ofcom had published “a damning assessment of James Murdoch’s behaviour in the running of News International”.
“That report only stopped short of declaring Sky as unfit and improper to hold a licence on the basis the Murdochs were a minority owner of Sky, not 100%, and James Murdoch was no longer playing an executive role at Sky,” said Mr Miliband. “Today, James Murdoch is back as chairman of Sky, and chief executive of 21st Century Fox.