A spokesman for the Prime Minister made it clear that Ms Greening’s support for a second referendum – or so called people’s vote – was unacceptable.
Ms Greening, a leading Remainer who was sacked by Theresa May, has wheeled in behind the campaign on the back of the much criticised Chequers plan for Brexit.
She joined fellow Tory rebel Phillip Lee, who resigned as a justice minister so he could oppose the government on Brexit and support a second referendum.
In an article for a national newspaper, Ms Greening said other senior Conservatives quietly back a second Brexit referendum.
Ms Greening she claimed Parliament is “gridlocked” over Brexit and the public should be given another vote that includes the option to remain in the European Union.
The Putney MP told BBC Radio 4’s Today she would campaign for Remain in any new vote. Asked if any other senior Tories backed a second referendum, she said: “Yes I believe so.”
Discussing the Prime Minister’s Chequers plan for Brexit she said: “I don’t think it can work. I think it was a genuine clever attempt at a compromise that could work.
“But in practice having looked through the detail now it just won’t and I cannot see how, going forward, the common rulebook will be workable in practice.
“What we need is a clear route forward that settles this European question once and for all.”
But Downing Street made it clear that it will not reopen the referendum.
A spokesman for the Prime Minister said: “The British public have voted to leave the EU. There is not going to be a second referendum under any circumstances.”
Meanwhile, Tory Brexiteer Sir Bernard Jenkin suggested Mrs May’s Chequers plan was “dead”.
He told Today: “I’m afraid it is neither beloved by Remainers or Leavers.
“It’s also quite likely to be either rejected by the EU or more demands will be made upon it so it will be even less acceptable.”
He described Ms Greening’s call for a second referendum as “a little ill-thought out”, saying: “If we wanted to extend the uncertainty for another long period this is one way of doing it.”
Ulster MP Sammy Wilson, whose Democratic Unionist Party backs Brexit and is holding up Mrs May’s majority, suggested Ms Greening should become a Lib Dem.
He said: “Now that Justine Greening supports Liberal Democrats’ alternative vote system, their call for a second referendum and their disdain for people’s verdict in 2016, perhaps she might be better joining the party which she seems more at home with.”