President Trump wants to recognize the military working dog injured during the raid that killed ISIS boss Abu Bakr al-Baghdadi in Syria last month, a source told The Post.

“It is the president’s desire to honor the dog. They are working out the details,” said the source, who claimed the commander-in-chief is even exploring a way to present Conan with a prohibited Purple Heart.

It could “swing the animal lovers vote” for Trump, one of the few presidents who has not had a pet dog at the White House, the insider said with a laugh.

Trump is intrigued by the historic possibility of presenting the Belgian Malinois with the revered medal, and is known for setting precedents, like his decision to appear at the Veterans Day Parade in Manhattan Monday, or his summit with North Korean dictator Kim Jong Un, said the source, who is close to the First Family.

Logistics have gotten in the way.

President Trump hinted at a ceremony with Conan at the White House this week in an Oct. 31 tweet. That became “a few weeks” while speaking at a rally in Tupelo, Mississippi the next day.

“The dog is working, probably involved in missions and everyone wants to keep the dog safe,” said the source. “When there is an opportunity, we can honor him and his handlers and the president is most certainly interested in doing that.”

Reps for the White House declined to comment, but did not deny a plan to present the dog with the medal.

Department of Defense rules currently forbid military working dogs from receiving the Purple Heart. The regulation was put in place after a dog named Chips was given one in 1943 for heroic action in World War II.

Conan, assigned to U.S. special forces, chased al-Baghdadi down a tunnel before the ISIS leader blew himself up with a suicide vest. The dog was injured during the explosion by exposed electrical wires. During a press conference announcing Baghdadi’s death, Trump heaped praise on the “beautiful” and “talented” dog.

In the days since, multiple human veterans and Purple Heart recipients have come forward to insist that President Trump reverse the DoD rules, saying dogs like Conan are as important as any human soldier.

“Do I believe Conan should receive a Purple Heart for actions on target? Absolutely,” Michael Bollinger, 26, a former Army Ranger now studying at Columbia University told The Post. “They’re out there with us every step of the way.”