The treasurer, who sits on both pension boards, is expected to make a formal motion for CalPERS in February.
CalPERS did not return a call for comment Wednesday.
The teachers' fund invests retirement benefits for more than 850,000 California public school teachers, workers and their families. It invests more than half of its assets in stocks but also has investments in bonds, private equity, real estate and other categories.
CalSTRS Chief Investment Officer Chris Ailman said Cerberus' investment in Freedom Group didn't raise flags because the fund's ethics policy was not expanded to include private equity investments until 2008, after the fund invested in Cerberus. Ailman said staff did not look at past purchases.
"At this point in time in 2008, we were very much focused on the external part of the portfolio in the emerging markets, and sadly, not so much on the U.S. equity portfolio," Ailman told the committee Wednesday. "I'd also point out in '08 as we did this, with the financial collapse, our attention very much became focused on mortgages, Wall Street and just the entire financial crisis at the time."
He said companies that manufacture firearms that are illegal in California could violate the fund's policy on human rights and human health.
Since the mid-1970s, the retirement system has factored political, environmental and social conflicts in reviewing potential investments. CalSTRS was one of early funds to divest from companies doing business with South Africa in an effort to end racial apartheid. The fund also avoids oil and energy investments in Iran and removed tobacco companies from its stock holdings years ago.