Sen. Jeff Flake speaks with reporters ahead of votes on Capitol Hill in Washington Thomson Reuters WASHINGTON (Reuters) - A bipartisan push in the Senate to protect undocumented people who immigrated to the United States as children is gaining momentum as lawmakers try to wrap up negotiations this month, Republican Senator Jeff Flake said on Tuesday.

"We're still working ... we're very close" to an agreement, Flake told reporters. He is one of a few Republicans and Democrats in the Republican-controlled Senate leading the effort to find legislation replacing the Deferred Action for Childhood Arrivals program that President Donald Trump is terminating.

In announcing last September that he was ending the Obama-era program, Trump challenged Congress to come up with a legislative replacement for the executive order that has been protecting around 700,000 "Dreamers" from the threat of deportation.

Trump said the current program will be terminated in March, but already some participants have seen their enrollments expire.

Democrats in Congress have been pushing to attach legislation restoring the immigration program to a must-pass spending bill either later this month or sometime next month.

(Reporting by Richard Cowan; Editing by James Dalgleish)