"close the possibility" is correct and usable in written English.
It is generally used to convey that an option or outcome is no longer viable. For example, "We had to close the possibility of taking a vacation this summer due to the pandemic."
"I never became a Buddhist or a Jain, I would never become a Franciscan monk; that would somehow close the possibilities, not open them," he told me at the Hirshhorn, looking very much the monk with his slight form, wire glasses and close-shaved head.
The donation brings closer the possibility of the Express titles endorsing Ukip at the election.
However under Malaysian law a person is banned from political activities for five years after the end of their sentence, closing the possibility of Anwar leading any campaign as he did in 2013.
Already, too, the increasingly open hostility between Syrian Sunnis and Shias has rekindled sectarian passions in Iraq, Lebanon and as far afield as Yemen, bringing closer the possibility of a direct clash between the Shia superpower, Iran, and big Sunni states such as Saudi Arabia and Turkey.
This chemical verification of previous theoretical results brings closer the possibility of utilising this phenomenon for implementing collision-based gates, signal tuning and programming of collision-based computers based upon excitable chemical reactions.
As government surpluses grow and the government comes closer to the possibility of closing down the Treasury securities market, the Bush Administration Treasury says it is considering ways to keep the market alive.
However, it didn't close off the possibility entirely.
This doesn't close off the possibility of elevated musicianship.
Mr Olmert met the Palestinian president, Mahmoud Abbas, and said that Israel and the Palestinians had "never been as close to the possibility of an agreement".
Mr. Olmert, under pressure at home to resign after additional allegations of personal corruption, said that Israel and the Palestinians "have never been as close to the possibility of an accord as we are today".
Nevertheless, a considerable military effort has been mounted in an attempt to close off the possibility that Mr. Hussein might escape to the north, by way of an underground command-and-control facility near Tikrit, his hometown.
