EXCLUSIVE

Feds investigating R. Kelly in Illinois are on the hunt for more sex tapes that allegedly show him with underage girls ... and prosecutors are doing everything they can to find footage.

Law enforcement sources tell TMZ ... the U.S. Attorney's Office for the Northern District of Illinois is interviewing parties closely associated with Kelly. We're told prosecutors have been asking about the possible existence of VHS tapes purportedly showing Kelly having sex with minors.

Rumors about an alleged stash of R. Kelly sex tapes have been floating around since Kelly went to trial on child porn charges back in 2008, but it's never been found ... not by law enforcement, anyway.

As we've reported ... the feds are building another case against Kelly in Illinois, which we're told is entirely separate from the 2 probes currently underway in New York -- one by the Eastern District and another by the Southern District.

We're told feds in Illinois are investigating Kelly on 3 different fronts: sex trafficking, tax evasion and obstruction of justice.

In terms of obstruction ... we're told prosecutors have been asking people close to Kelly an array of questions focusing on his 2008 trial, believing Kelly and his handlers may have pressured witnesses. Some of the questions involve alleged payoffs to prevent witnesses from testifying in court or speaking out publicly.

We reached out to the U.S. Attorney's Office, but it declined to comment.