The meeting was sought after the Udon Thani provincial court approved arrest warrants for six people allegedly involved in the Jan 22 shooting. Of the six, four are reportedly soldiers.
The police earlier wrote to the army asking it to send the four soldiers to face charges.
According to the source, Pol Gen Adul showed an investigation report to Gen Prayuth and promised police would conduct their inquiry in a transparent manner.
The source said that in addition to the four, an army lieutenant colonel attached to the 9th Infantry Division was also implicated in the attack on Mr Kwanchai.
A source in the army said three of the suspects are attached to the 19th Cavalry Battalion.
He identified them as 2nd Lt Pratya Chanrodpai, SMG Wirot Pimsing and SMG Mawin Yangbua. The other was identified as Sgt Chanon Taptimtong, of the 9th Infantry Division.
Police recently arrested two more suspects. Matuemang Mase was caught in Narathiwat and was alleged to be the gunman, while the other was identified as Banchong Tarathong.
Army spokesman Winthai Suwaree said yesterday the army and the suspects’ superiors are in the process of bringing the four soldiers to meet police for questioning.
He said military officers from the Judge Advocate-General's Department would be present during questioning.
If indicted, the soldiers would stand trial in a civilian court, not a military one because the other alleged accomplices are civilians, the spokesman said.
Maj Gen Pairote Thongma-eng, commander of 9th Infantry Division, said the army hasn't set up a probe committee.