Lindsey Graham isn’t exactly a huge fan of Donald J. Trump.

He ran against him for the Republican presidential nomination in 2016. Trump hurled a few insults at him. Graham said some unkind things in return.

But the U.S. senator from South Carolina is trying to implore the president to do the right thing — and avoid naming a politician to become the next director of the FBI.

Sen. Graham is talking specifically about Texas Republican U.S. Sen. John Cornyn, who has emerged as one of the favorites to succeed James Comey at the FBI, whom Trump fired this past week.

Cornyn could face stiff resistance in the Senate if Trump selects him, even though Cornyn has been part of the “world’s greatest deliberative body” for some time now. He’s known to have friends on both sides of the aisle.

But the FBI needs a decidedly non-political director in this difficult time, Graham said. “I think it’s now time to pick somebody that comes from within the ranks or is such a reputation that has no political background at all,” he said. “John Cornyn is a wonderful man. Under normal circumstances, he would be a superb choice to be FBI director. But these are not normal circumstances. We’ve got a chance to reset here as a nation.”

“Reset” is a mild term. I prefer to think the FBI leadership needs a major overhaul.

It’s not that Comey was a bad director, despite what the president said about him. Word filtering out of Washington by those who know Comey well say the president’s description of him as a “showboat” just doesn’t square with the man’s reputation.

Sen. Graham’s assessment of a successor, though, is on target. The FBI needs to be led by someone who knows how to pursue an investigation to a comprehensive conclusion. I would have thought Comey is capable of doing that, which likely got him in trouble with Trump.

Cornyn may have great political skill. The agency needs someone who would cooperate fully with a special prosecutor — whom the Justice Department should name to handle this probe.

Sen. Cornyn’s political background is precisely the wrong fit for this job — at this time.