Bae plans on playing in Hawaii next week on the PGA Tour, according to his manager.
According to Yonhap news agency, Bae's mother said the golfer had his overseas travel permit extension request rejected by the Military Manpower Administration.
The golfer must return to Korea by the end of January or could be prosecuted as his current permit expires soon.
"(Bae) is seeking legal counsel to work through the military issues in Korea," the 28-year-old golfer's manager said on Friday.
"He has a valid green card, and Sang-moon intends to stay in the United States as long as it is lawful to do so and play on the PGA Tour this year, beginning with next week's Hyundai Tournament of Champions at Kapalua Resort on the Hawaiian island of Maui.
"As this is an ongoing legal matter, he will make no additional statements until the issue is resolved," he added.
All South Korean men between 18 and 35 must complete two years of military service.
Bae made his PGA Tour debut in 2012 and was granted US residency two years ago.