Senate Republicans are eyeing a vote on the floor on Brett Kavanaugh’s Supreme Court nomination next week.

Senators, while coming out of a closed-door caucus lunch, acknowledged the situation remains fluid, but said they expected to be in session through the weekend to run out the procedural clock, a move that would allow them to wrap up Kavanaugh’s nomination next week.

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GOP Sen. John Cornyn John CornynQuinnipiac polls show Trump leading Biden in Texas, deadlocked race in Ohio The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight MORE (Texas), the No. 2 GOP senator and member of leadership, told reporters that if Kavanaugh could get out of the Judiciary Committee on Friday they would be able to be done with the nomination "by the first part of next week.”

"We need to have a mark up and my hope would be we could have that mark up as early as Friday and be on the floor this weekend," Cornyn told reporters.

Sen. Johnny Isakson Johnny IsaksonLobbying world Loeffler paints herself as 'more conservative than Attila the Hun' in new campaign ad Georgia GOP Senate candidates cite abortion in pushing Ginsburg replacement MORE (R-Ga.) said he was planning to be around until Tuesday to finish Kavanaugh’s nomination.

“If you plan to do something before next Tuesday I wouldn’t plan on it,” Isakson said.

GOP Sen. John Thune John Randolph ThuneSenate passes resolution reaffirming commitment to peaceful transition of power Susan Collins faces political land mine with Supreme Court fight Abortion stirs GOP tensions in Supreme Court fight MORE (R-S.D.) initially told reporters that a vote could happen on Tuesday. He later hedged after the lunch saying it depends on how much Democrats drag out the procedural clock.

If the Judiciary Committee sent Kavanaugh's nomination to the full Senate on Friday, that would allow Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump 'no longer angry' at Romney because of Supreme Court stance On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline The Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power MORE (R-Ky.) to file cloture as early as Saturday and hold an initial vote as early as Monday.

McConnell did not give a specific timeline on Kavanaugh’s nomination during a weekly press conference only saying they would vote in the near future.

"I believe he'll be confirmed, yes," he told reporters.

No schedule on Kavanaugh’s nomination has been formally announced beyond a Thursday hearing where Kavanaugh and Christine Blasey Ford, a woman accusing him of sexual assault, are scheduled to testify before the Judiciary Committee.

Cornyn told reporters Monday evening that it was possible a committee vote could happen by Friday. If the Judiciary Committee wants to vote on Friday, committee chairman Chuck Grassley Charles (Chuck) Ernest GrassleyGOP lawmakers distance themselves from Trump comments on transfer of power The Hill's 12:30 Report: Ginsburg lies in repose Top GOP senators say Hunter Biden's work 'cast a shadow' over Obama Ukraine policy MORE’s (R-Iowa) staff would have to notice the vote on Tuesday.

Senate Majority Leader Mitch McConnell (R-Ky.) expressed confidence that the Senate would confirm Kavanaugh.

“We’re going to be moving forward. I’m confident we’re going to win, confident that he’ll be confirmed in the very near future,” McConnell told reporters.

McConnell did not specify when Kavanaugh's nomination will come to the Senate floor, except that they would take it up in the "near future."

A GOP aide, asked about the Tuesday vote timeline, stressed that a final decision had not been made but to not make weekend plans.

Senators discussed strategy for Kavanaugh during their closed-door lunch.

Grassley told his colleagues at the lunch to prepare to be in session this weekend, Sen. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (R-Tenn.) told reporters.

Cornyn, asked if Grassley specifically said to plan to be in session during the weekend, quipped: "I'm telling you."

"We're going to be here this weekend," he added.

Several other senators said that a final decision had not been made but that they expect to be in session to try to run out the procedural clock on Kavanaugh's nomination over the weekend.

"I'll be here. ... I think that it's going to be pretty hard to move this along without having votes on certainly Friday and Saturday," GOP Sen. Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (Utah) told reporters.

GOP Sen. John Kennedy John Neely KennedyMORE (La.) asked about the weekend told reporters, "I think we are going to be in session."

The decision to move forward with Kavanaugh's nomination comes even as he appears short of the simple majority support needed to be confirmed.

GOP Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (Ariz.) has yet to say if he will support Kavanaugh's nomination or the Judiciary Committee voting this week on the nomination.

If he voted against the nomination in committee it would leave Kavanaugh without the simple majority support needed to be confirmed.

Cornyn said leadership is in constant communication with Flake, who has not voted this week, but added that he hadn't yet heard demands for more time between a hearing and a vote.

Kavanaugh would need a simple majority to be confirmed by the full Senate.

In addition to Flake, GOP Sens. Lisa Murkowski Lisa Ann MurkowskiOVERNIGHT ENERGY: House passes sweeping clean energy bill | Pebble Mine CEO resigns over secretly recorded comments about government officials | Corporations roll out climate goals amid growing pressure to deliver The Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Abortion stirs GOP tensions in Supreme Court fight MORE (Alaska) and Susan Collins Susan Margaret CollinsThe Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power Billionaire who donated to Trump in 2016 donates to Biden Credit union group to spend million on Senate, House races MORE (Maine) remain undecided and aren't expected to make a decision until Thursday's hearing.

Updated at 4:30 p.m.