(CNN) Sen. Jeff Flake is warning that he may block votes on the nominations of all of President Donald Trump's pending appellate court nominees unless he gets favorable action on two issues unrelated to the judiciary.

According to one source, Flake wants to spur discussions on travel restrictions to Cuba as well as issues related to tariffs.

"We're discussing it," the Arizona Republican said in a brief interview with CNN as he came out of an immigration negotiation.

Flake sits on the Judiciary Committee, where Republicans have a slim 11-10 advantage over Democrats. If he does not relent, he could bring the work of the powerful committee to a halt as it applies to appellate court nominees, who are often voted out on party lines.

Confirming these influential circuit court nominees has been a top priority and bragging point for Senate Majority Leader Mitch McConnell and Trump.

So far, the Senate has pushed through an unprecedented number of appeals court nominees. Indeed, McConnell tweeted publicly in January: "@potus was able to seat more Circuit Court judges in the 1st year of his presidency than anyone in history."

On Wednesday night, Judiciary Chairman Chuck Grassley, an Iowa Republican, acknowledged that if Flake moved to block the nominees, his hands could be tied.

Grassley told CNN he will not schedule votes on these nominees until Flake's issues are resolved and he is on board.

"If it is a controversial one, we probably would have to have all 11 Republicans. So if one Republican wouldn't vote, and it's 10 to 10, then we're not going to take it up," he said.

But Grassley added that the Senate nominations calendar is so full right now he doesn't feel any pressure for the Judiciary Committee to move anyone out until September.

"I could probably wait for a month to vote any more judges out, so there is nothing immediately of concern to me as far as the work of the committee is concerned," he said.

Grassley noted he hadn't spoken directly with Flake on the matter.

"So we can just delay and delay and delay," Grassley said. "If we don't vote for any more judges that Flake doesn't want to vote for until September, we still probably got plenty to do."

Flake, who has announced he will not be seeking re-election, has been an outspoken critic of Trump. He could exercise rare leverage over the President by holding up these nominees.

In addition, GOP leaders recognize that at this point, because of the absence of Sen. John McCain, his fellow Arizona Republican, Flake has extraordinary power to affect the confirmation of nominees not just in committee but on the floor too.

Even if these nominees were voted out of committee -- or if leaders used procedural tools to move them to the floor without a vote of approval from the Judiciary Committee -- Flake could help block them on cloture, the procedural motion to end debate that needs a majority of senators.

If Flake voted with Democrats on cloture, he could defeat the motion to advance the nominee 49-50.

Sen. John Cornyn of Texas, who is the second-ranking Republican in the Senate and a member of the Judiciary Committee, said he was not aware of Flake's specific concerns but wanted to talk to him to see if they could be resolved.

A source familiar with Flake's issues complained that it is a "bizarre situation where a senator is holding nominations hostage for his pet projects."

Kristine Lucius, a longtime Democratic staffer on the Senate Judiciary Committee who is now the executive vice president for policy at the Leadership Conference on Civil and Human Rights, welcomed the news of Flake's hesitation.

"Senators are supposed to be making independent decisions about the suitability of any nominee for a lifetime appointment, " she said and criticized Republicans for voting in "lockstep" for every one of the President's nominees.

"There would be nothing inappropriate for a senator to start weighing those decisions more carefully," she said.