Executives from fund giants BlackRock Inc., Vanguard Group Inc., J.P. Morgan Chase & Co. and Invesco Ltd. earlier this month met with Securities and Exchange Commission Chairman Mary Schapiro to talk about money market reforms, the Wall Street Journal reports.

Specifically, the fund firms reportedly support a weaker measure of Schapiro's plan to allow investors to redeem only 95% to 97% of their holdings at once, with the rest payable after 30 days. Rather than lock up a portion of investors' money for 30 days, the companies would charge investors a fee to withdraw money during a "liquidity event," such as the 2008 financial crisis, according to the pub, citing people familiar with the matter.

The SEC, which called the meeting, was reportedly receptive to the idea.

Another meeting is scheduled in June.