Senate Majority Leader Harry Reid signaled Friday that the Senate may take up the controversial nomination of Leslie Southwick to the U.S. Court of Appeals for the 5th Circuit.

Reid is seeking a vote to limit debate on the nomination Tuesday. If that succeeds, the Senate would vote on whether to confirm Southwick.

“Both Sen. [Patrick J.] Leahy [D-Vt.,] and I have said that when the Republicans tell us they want to move on that, we would do that,” Reid, D-Nev., said, referring to the Judiciary Committee chairman. “So, some time next week, I’m more than likely going to move to that matter. So I want everyone to know that, in fact, is the case.”

Senate Republicans have assumed they would need to round up a filibuster-proof supermajority of 60 votes to win confirmation for Southwick. It’s unclear whether Southwick’s supporters have done so. A spokesman for Reid declined to say whether Democrats would filibuster the nomination. A Senate Republican aide said there is no agreement on a time limit for debating the nomination.

Southwick’s opponents have highlighted his participation in two cases while he was a Mississippi state appeals court judge. One decision upheld the reinstatement of a social worker who used a racial epithet to describe a colleague. Critics also say Southwick’s track record is replete with evidence that he is hostile to African-Americans and disadvantaged people, and too pro-business.

The Senate Judiciary Committee voted 10-9 nearly along party lines Aug. 2 to approve the nomination. California Democrat Dianne Feinstein joined all nine committee Republicans in voting for the nomination.