Some Senate Republicans fear their Democratic counterparts will selectively leak parts of the FBI's final report about Supreme Court nominee Brett Kavanaugh in order to make him look bad just as the Senate prepares to vote on him.

As of Tuesday, the plan was to only have the report go to senators so they can decide whether to support Kavanaugh, and vote on him sometime this week. Both Republican and Democratic Senate leaders seem to agree on that plan.

[Click here for complete Kavanaugh coverage]

But that has some Republicans worried about partial leaks aimed at turning the public against Kavanaugh.

“I hope there is going to be some way for all of you to see parts of it,” Sen. Bob Corker, R-Tenn., told reporters Tuesday. “Because I’m afraid it’s going to be selectively leaked out and each side will use the piece that works best for them.”

Sen. John Kennedy, R-La., agreed that the report should be released so the public can weigh in based on the report itself, not others' interpretation of the report.

“The report will be done this week and I think its contents should be made available to the American people,” Kennedy said. “I trust them to decide.”

Kennedy said his preference is that the public weighs in, and he believes many of his fellow GOP lawmakers want that, too. He also agreed with Corker about the danger of Democratic leaks.

“We need to take steps that ensure that the American people know what is in the report in its totality as opposed to having people just leak portions of it,” Kennedy said.

Senate Majority Leader Mitch McConnell, R-Ky., said Tuesday the report will only to go to senators, and he wants them to read it quickly and decide.

“We’ll get an FBI report soon,” McConnell said. “It will be made available to each senator, and only senators will be allowed to look at it. And that is the way these reports are always handled, these background checks, through the Judiciary Committee.”

[Also read: When will the FBI interview Christine Blasey Ford?]

McConnell’s decision was announced after Sen. Dianne Feinstein, D-Calif., the ranking member on the judiciary panel, said she also opposes the public release of the report, which will include details of at least two sexual misconduct allegations leveled against Kavanaugh and which date back more than three decades. Feinstein questioned whether senators would be able to make the report public.

"My understanding is it cannot be initially," Feinstein said Tuesday. "I don't know what’s going to be in it. After that, we’ll find out."

But Sen. Richard Blumenthal, D-Conn., who sits on the Judiciary committee, argued that it should be released.

"Yes, there's no question the FBI report should be released so the American know what the findings were," Blumenthal said.

Sen. John Cornyn, R-Texas, said Tuesday while the report itself would not be publicly released, some kind of statement would be issued about the contents.

The FBI was ordered by the Trump Investigation to conduct a supplementary FBI background check on Kavanaugh at the request of a handful of key GOP lawmakers who are undecided on the nominee. Sen. Jeff Flake, R-Ariz., and others have said they won't support Kavanaugh without that report.

Republicans anticipate the report will not include anything incriminating about Kavanaugh, and Cornyn indicated some kind of summary could be released to clarify what it found.

"There is going to have to be some sort of announcement about what this supplemental FBI investigation has yielded," Cornyn said.

Laura Barron-Lopez contributed