By law, the CIA controls all overseas espionage operations. But the CIA and Special Forces were both founded by men who had served with the OSS (Office of Strategic Services) during World War II and the relationship continued after the OSS veterans retired from their CIA and Special Forces careers.
The army wants to more aggressively use Special Forces troops for espionage so that the "battlefield can be prepared" more quickly. This is seen as necessary in order to effectively run down fast moving terrorist organizations. Currently, the Special Forces depends on the CIA to do the espionage work in advance of Special Forces A-Teams arriving. In practice, some Special Forces troops are often there, along with CIA personnel, doing the advance work of finding who exactly who is who, what is where and, in particular, who can be depended on to help American efforts. The CIA has not made a big stink about this new Department of Defense effort, if only because the CIA short of people and is still aggressively recruiting people for anti-terrorism operations. Besides, a prime source of new CIA agents has long been former, or retired, Special Forces operators. With the new espionage training Special Forces troops are getting, the CIA will be able to hire these guys later and put them to work without having to train them in a lot of espionage techniques.
In peacetime, Special Forces troops spend a lot of their time (up to half in some years) overseas providing training and advice for foreign armed forces. The Special Forces troops doing this work take careful notice of their surroundings and are debriefed when they get back to the United States. These Special Forces reports form some of the most accurate and up-to-date information on the local armed forces in foreign nations.
The Department of Defense has announced that Special Forces troops will be trained for plain clothes, or uniformed, espionage work in foreign counties. The Special Forces have unofficially been doing this sort of thing for decades, sometimes at the request of the CIA. In 1986, the Special Forces even established an "intelligence operations" school to train a small number of Special Forces troops in the tradecraft of running espionage operations in a foreign country. In practical terms, this means recruiting locals to provide information and supervising these spies, agents and informants.