Gen Saiyud Kerdphol, a former supreme commander, said Gen Prem had asked him to draft a royal command to that effect.
The group issued a statement on Friday, urging Gen Prem to take action.
Gen Saiyud, 92, said His Majesty was the heart and soul of the nation. All organs — whether they are the government, armed forces and courts — performed their duties in his name.
When a government cannot perform its duty as pledged when it took office, he said, questions arise about what should be done to prevent this from affecting His Majesty.
Since His Majesty is above politics, a responsible person must propose the draft in an appropriate way. If anything goes wrong, the person countersigning it must take responsibility.
Some critics have said that that the group risks disturbing His Majesty by advancing such a proposal, but the Man of State group believes the opposite is true, the retired general said.
"What we're doing will enhance his charisma, unlike a 'key organisation' which has done nothing," he said.
In a video posted on YouTube of one of the group's meetings, its main grievance was the army's "lack of action" in solving the crisis.
"Watching the situation without doing anything is what disturbs His Majesty," he said.
Gen Saiyud denied that his group had any links to the Rubbish Collection Organisation, which has promised to take a draconian approach to apply lese majeste law to people they believe are anti-monarchist.
The Man of State group was formed on Jan 28 and a video of its meeting was posted the following day. Its members believe the current crisis needs to be solved by the intervention of the army and His Majesty the King.
The group consists mainly of retired high-ranking generals, government officials and academics. They include former air force chief ACM Gun Pimarnthip, ex-army chief Gen Wimol Wongwanich, former naval commander Adm Vichet Karunyavanij, ex-naval chief of staff Gen Suravudh Maharom, lawyer Amorn Chantarasomboon, political science scholars Pramote Nakhonthap and Chai-Anan Samudavanija, and former foreign affairs minister Surapong Jayanama.