During his unannounced visit, Hagel is not expected to meet with President Hamid Karzai, but will talk with Afghanistan's defense and interior ministers, the Washington Post reported.
The lack of an official nod to the Afghan president appears to suggest U.S. officials believe Karzai is not likely to relent any time soon on last-minute demands he wants met before agreeing to sign a security agreement.
Hagel is also expected to meet with U.S. troops, the Pentagon said in a statement.
Hagel is the latest senior U.S. official to visit the country in recent weeks, Khaama Press reported.
Earlier this week, U.S. special envoy for Afghanistan and Pakistan Jim Dobbins reported Karzai had not backed off demands that include releasing all Afghans held by the United States at the Guantanamo Bay, Cuba, prison camp and ending all strikes in the country.
The stalled agreement comes in advance of Afghan presidential elections and the drawdown of foreign troops in the coming year. Lack of an agreement could threaten international support for Afghanistan during that crucial period, U.S. National Security Adviser Susan Rice said during a visit to Kabul last month.
The chairman of the Senate Armed Forces Committee, Sen. Carl Levin, D-Mich., urged President Obama in a letter Thursday to ignore Karzai and continue planning to keep U.S. troops in Afghanistan after 2014, under the assumption the new Afghan president will sign the agreement.