The source said Seoul and Washington are also seeking the best timing to announce the results of their sensitive missile talks.
Korea is banned from developing ballistic missiles with a range of more than 300 kilometers (186 miles) and a payload heavier than 500 kg (1,102 pounds) under a 2001 deal with the U.S.
Seoul has been seeking to extend the range of its missiles to at least 800 kilometers in order to cover all of North Korea, which is armed with missiles of various ranges.
In its final months in power, South Korea's Lee Myung-bak administration apparently believes that a deal on longer-range missiles will be one of its key diplomatic and political achievements to help broaden support from the ruling camp's conservative base.
The U.S. has been tepid, however, citing concerns over a negative impact on its nonproliferation efforts.
China is also keeping an wary eye on South Korea's drive.
Nonetheless, it appears difficult for the U.S. to ignore its Asian ally's continued request.
The source refused to specify the newly agreed range of South Korea's ballistic missiles.
The White House also said it has "no information to provide."
Another source said the U.S. is expected to allow South Korea to develop ballistic missiles with a range up to around 550 km and instead expand comprehensive deterrence against North Korea's missile threats.
U.S. officials have emphasized the importance of partnerships with South Korea and other allies in regional missile defense networks.
"We are also continuing to discuss BMD bilaterally with the Republic of Korea," Frank A. Rose, deputy assistant secretary of state at the Bureau of Arms Control, Verification and Compliance, said in Berlin, Germany, said earlier this week, using the official name for South Korea.
BMD stands for ballistic missile defense.