A source close to Los Angeles law enforcement tells FOX411 that several women have come forward to say Charlie Sheen had sex with them without divulging his HIV status, after Sheen said in an interview Tuesday that he told every one of his sex partners he was HIV positive before they had sex. 

“They are trying to come up with a list,” the insider said. “They envision a lengthy criminal investigation. They are not ignoring it, because they can't. This is categorized as highly sensitive material.”

One of the problems so far is that even though they have contacted law enforcement, nobody wants their names on the list.

“Four or five different young ladies came forward saying they don't want their names out,” the insider said, adding that won’t stop law enforcement from doing “a thorough investigation. It will be weeks before anything comes out publicly, that's a conservative timeframe. “

“It is almost impossible for the DA’s office not to file based upon his comments,” the source said, referring to Sheen’s admission he had been having sex with women while HIV positive, including unprotected sex with two women he said knew of his status and were under his doctor’s care.

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Another source close to the situation told FOX411 that Sheen had sex with “several women” just last week, and didn’t tell them he was HIV positive.

Bree Olson, who lived with Sheen in 2011, said in an interview Tuesday with Howard Stern that Sheen never told her, either.

“He never said anything to me,” she said. “I was his girlfriend. I lived with him. We were together. We had sex almost every day for a year.”

Sheen and Olson split in April 2011. Sheen's manager said he wasn't infected when they were together.

“The more calls the DA receives inquiring whether a criminal investigation is in place pushes them to file criminal charges," the source close to LA law enforcement said. "Charlie has been bragging for years about his sexual conquests. Unfortunately, he also admitted that he’s known he was positive for at least four years. Obvious questions to follow are what did he do to protect his partners?”

Sheen’s rep had no comment.

When asked if there is an investigation underway, an LAPD spokesperson told FOX411 “There is nothing yet” and told us to call back later.

A spokesperson for the DA’s office replied in an email: “There is no criminal complaint against Charlie Sheen.” 

Exposing someone to HIV is a felony only if intent to infect that individual can be proven, as stated in California Health and Safety Code Section 120291: “Any person who exposes another to the human immunodeficiency virus (HIV) by engaging in unprotected sexual activity when the infected person knows at the time of the unprotected sex that he or she is infected with HIV, has not disclosed his or her HIV-positive status, and acts with the specific intent to infect the other person with HIV, is guilty of a felony punishable by imprisonment in the state prison for three, five, or eight years. Evidence that the person had knowledge of his or her HIV-positive status, without additional evidence, shall not be sufficient to prove specific intent.”

Fox News.com Reporter and FOX411 host Diana Falzone covers celebrity news and interviews some of today's top celebrities and newsmakers.  You can follow her on Twitter @dianafalzone.