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(CNN) —  

The Senate will hold a vote on immigration legislation, including whether to extend the Deferred Action for Childhood Arrivals program, next month, but only if lawmakers can reach a deal before the end of January, Majority Leader Mitch McConnell said Wednesday.

“There are bipartisan discussions in the Senate, involving the administration, about improving border security, interior enforcement and reforming important parts of our broken immigration system, including addressing the unlawfully established Deferred Action for Childhood Arrivals program,” McConnell said in a statement.

“If negotiators reach an agreement on these matters by the end of January, I will bring it to the Senate floor for a free-standing vote,” he said.

McConnell’s statement came after Arizona Republican Sen. Jeff Flake had said he received a commitment for a vote on immigration. Flake’s statement and tweet came after he voted for the GOP tax bill that passed early Wednesday morning.

Flake had been hesitant on the tax package, but in negotiations said one of his requirements had been a commitment to progress on a plan to provide a permanent legislative version of DACA, which President Donald Trump is ending.

“While I would have written a much different bill, this bill lowers the corporate tax rate in a manner that makes us globally competitive. I am also pleased that the Majority Leader has committed to bring the bipartisan DACA bill we are currently negotiating to the Senate floor in January,” Flake said.

White House meeting

Flake, a long-time immigration reform advocate, met Wednesday at the White House with key Senate negotiators and Trump’s chief of staff John Kelly, three sources familiar with the meeting confirmed. Details of the meeting were first reported by Politico.

The meeting was “very productive” and “moved the ball forward” toward a possible deal in the new year, a source familiar with the meeting said.

According to one of the sources, Kelly indicated to the group that the White House would be putting together some of its priorities for a deal after the meeting.

An earlier release from the White House about its immigration wish-list was a comprehensive compilation of virtually all of what conservatives want on immigration, and was written off by Democrats as containing multiple poison pills. The White House has not yet indicated where its red lines are on those principles.

In the meeting, a group of senators, which includes Flake, Senate Democratic Whip Dick Durbin, Democratic Sen. Michael Bennet, and Republican Sens. Lindsey Graham, Thom Tillis, James Lankford and Cory Gardner, discussed the progress of their negotiations, which have included regular meetings in Durbin’s office.

The group has resolved some issues with how to legislate DACA, which protected young undocumented immigrants brought to the US as children from deportation, but is still heavily negotiating border security measures to pair with it and how to handle Trump desire to reform “chain migration,” or family-based migration.

The meeting also included other key Republicans like Senate Majority Whip John Cornyn, who have been in contact with the members of the working group.

CNN’s Lauren Fox contributed to this report.