They are Pol Gen Somyot Poompanmoung and Pol Gen Aek Angsananont.
Pol Gen Somyot said on Friday that he sent his profile and written vision to acting police chief Pol Gen Watcharapol Prasarnrajkit and he would accept the decision of his supervisor.
Pol Gen Aek said that as he was among possible contenders for the job, Pol Gen Watcharapol ordered him to send up to two A4 pages explaining his vision on the management of the force by Friday.
He had no idea when Pol Gen Watcharapol would convene a meeting of the Board of the Royal Thai Police Office to consider the appointment of the new police chief.
After the May 22 coup, Pol Gen Adul Saengsingkaew, former police chief, was moved out to supervise special affairs for the National Council for Peace and Order at Government House.
The acting police chief is due to retire at the end of September, and has the authority to nominate his successor to the board for official appointment.