Mr. Green openly supported Remain during the 2016 referendum campaign.
However, in an article for The Mirror, he said: "I think there are strong and important reasons against a new referendum that demonstrates why it simply can not happen."
First, Green argued that there simply is not enough time to get a bill that describes a second referendum in Parliament before the UK leaves the EU on March 29, 2019.
He explained: "An additional referendum would need an Act of Parliament, and probably other" secondary "laws by its side.
"There simply is not enough time for this to be done, properly, before March of next year."
The bill that facilitated the 2016 referendum took five months to pass in Parliament.
For his second point, Mr. Green said that the result of 2016 has been strengthened and legitimized by Parliament.
He affirmed: "Leaving the EU no longer depends only on the result of 2016.
"Now it also depends on the decisions of the Supreme Court, the Parliament and the electorate."
The Government's Brexit bill was approved by Parliament in June after winning a vote of 319 to 303.
Mr. Green noted how bitter the 2016 referendum campaign was and said a second would "make things worse".
To support this position he quoted the Financial Times writer, Robert Shrimsley, who commented: "If the previous campaign was ugly and divisive, imagine the following."
He also pointed out that the public could simply vote for Brexit again.
He said: "There is no particular reason to believe that the electorate will side with Remain, no matter how much the opponents of Brexit want him to do so."
Recent surveys suggest that the party is still divided in half on whether to leave the EU.
Mr. Green added that a second referendum, if it led to a result different from the first, could lead to a battle of mandates between Brexiteers and Remainers.
The Prime Minister, Theresa May, has firmly rejected the possibility of a second Brexit vote.
Speaking at the Conservative Party conference earlier this month, he said: "A second referendum would be a politician's vote.
"Think for a moment what it would mean for democracy if the people of this country made this decision, the politicians will try to nullify it."