The request would increase the number of military personnel who will be mobilised in the capital next Monday to 40 military companies, or 6,000 soldiers, the source said on Monday.
Internal Security Operations Command (Isoc) spokesman Banphot Phunphian earlier said at least 20,000 policemen would be involved in a joint police-military operation to prevent and handle any incidents on the Jan 13 anti-government rally.
The source said army chief Prayuth Chan-ocha had ordered all soldiers taking part in the operation not to carry weapons. They would be armed with shields and batons only.
Meanwhile, Lt Gen Surachet Chaiwong, deputy chief of staff, on Monday afternoon paid an inspection visit on behalf of Gen Prayuth to five companies of soldiers who began to help police maintain peace during the protracted protest and guard Government House on Saturday.
He said Gen Prayuth and other high-level army officers were concerned about the safety of their men and stressed that they must adhere to discipline as core of the operation and perform their duties with caution to avoid confronting the protesters.