It appears that the FBI investigated Tamerlan Tsarnaev in 2011. Here’s the FBI statement about that encounter.
The two individuals believed to be responsible for the Boston Marathon bombings on Monday have been positively identified as Tamerlan Tsarnaev, now deceased, and Dzhokar Tsarnaev, now in custody. These individuals are brothers and residents of Massachusetts. Tamerlan Tsarnaev was a legal permanent resident and Dzhokar Tsarnaev is a naturalized U.S. citizen. Charges have not yet been filed against Dzhokar Tsarnaev and he is presumed innocent.
Tamerlan Tsarnaev, age 26, was previously designated as Suspect 1, wearing a black hat. Dzhokar A. Tsarnaev, age 19, was designated as Suspect 2, wearing a white hat. Both were born in Kyrgyzstan.
Once the FBI learned the identities of the two brothers today, the FBI reviewed its records and determined that in early 2011, a foreign government asked the FBI for information about Tamerlan Tsarnaev. The request stated that it was based on information that he was a follower of radical Islam and a strong believer, and that he had changed drastically since 2010 as he prepared to leave the United States for travel to the country’s region to join unspecified underground groups.
In response to this 2011 request, the FBI checked U.S. government databases and other information to look for such things as derogatory telephone communications, possible use of online sites associated with the promotion of radical activity, associations with other persons of interest, travel history and plans, and education history. The FBI also interviewed Tamerlan Tsarnaev and family members. The FBI did not find any terrorism activity, domestic or foreign, and those results were provided to the foreign government in the summer of 2011. The FBI requested but did not receive more specific or additional information from the foreign government.