Sen. Lindsey O. Graham (R-S.C.) speaks to reporters in the U.S. Capitol last week. (Joshua Roberts/Reuters)

Sen. Lindsey O. Graham (R-S.C.) said Tuesday he considers the relationship between President Trump and Attorney General Jeff Sessions to be “beyond repair” — but cautioned that a replacement would have to promise the Senate he would allow special counsel Robert S. Mueller III to complete his investigation.

Graham’s comments, made in a television interview, come as a growing number of Republican senators are acknowledging the possibility Sessions could soon be fired by Trump, who has repeatedly criticized his performance.

In an interview with The Washington Post, Sen. Richard C. Shelby (R-Ala.) said the relationship between Sessions, a former senator from Alabama, and Trump is “challenged.”

“I wish it were not so,” Shelby said. “Sessions is an old friend of mine, served alongside him for 20 years. There’s a toxic relationship.”

Asked whether Sessions will last as attorney general, Shelby said: “Nothing lasts forever. I don’t know.”

Graham raised eyebrows last week when he seemed to give Trump his blessing to fire Sessions, telling reporters the president is “entitled to an attorney general he has faith in.”

Trump has repeatedly derided Sessions publicly for recusing himself from the investigation of Russian interference in the 2016 election, a probe Trump calls a “witch hunt.” That has prompted widespread speculation Trump would name a replacement who would shut down the probe, now being led by Mueller.

During an appearance Tuesday on NBC’s “Today” show, Graham stood by his assessment that Trump should have an attorney general he trusts but stressed an important caveat.

“You have to replace him with somebody who is highly qualified and will commit to the Senate to allow Mueller to do his job,” Graham said. “Nobody is going to take Jeff’s place that doesn’t commit to the Senate and the country as a whole that Mueller will be allowed to finish his job without political interference.”

Graham said he understands Trump’s frustration with Mueller’s investigation but added: “Here’s what I believe about Mueller: He’s a fine man. He’s not on a witch hunt. Let him do his job.”

Mueller is investigating whether Trump’s campaign coordinated with Russia during the 2016 election and whether Trump has obstructed the probe.

Graham said he has seen “no evidence of collusion” to this point, but added: “At the end of the day, if there is collusion between the Trump campaign and the Russians, that will be it for me.”

Tensions between Trump and Sessions flared last week after Trump said in an interview with Fox News that Sessions “never took control of the Justice Department.” Sessions, a former senator from Alabama, pushed back hours after Trump spoke, saying the Justice Department would not be “improperly influenced by political considerations” under his leadership.

Some Republican senators have counseled Trump against replacing Sessions, cautioning it would be difficult to win Senate confirmation for a replacement while the Mueller investigation is ongoing. But a growing number are speaking out about the possibility of new attorney general in the not-too-distant future.

Graham said Tuesday the rift between Trump and Sessions is “much deeper” than their differences over the Mueller investigation but would not elaborate.

Sen. Roy Blunt (R-Mo.) told The Post turnover is common in presidential administrations.

“At the end of the first two years, changes happen because people are ready to leave, sometimes because their boss is ready for them to leave,” Blunt said. “We wish the best for him [Sessions], but as any administration would show, Cabinet members seldom last the entire administration, and this is clearly not an exception.”

Sen. Marco Rubio (R-Fla.) said he hopes Sessions “doesn’t leave, certainly not before the election.”

“Attorney generals don’t always serve for the two terms of the president, so it’s possible that in the second term there would be somebody different,” Rubio said. “That would be par for the course with other administrations. But I think Jeff Sessions is doing a good job and should continue.”