Under the present financial structure, they pay all of their profits to the Treasury in the form a dividend, to compensate taxpayers for the risk they bear in providing a financial backstop.
Investors who own the shares claim the post-crisis set-up is unfair and untenable. Several have taken legal action against the Treasury.
Moelis claimed its recapitalisation plan would allow the government to realise between $75bn and $100bn in cash by exercising warrants, a structure it likened to the post-crisis resolution of the bailed-out insurer AIG.
Private investors would plough additional funds into the two groups as part of the proposed recapitalisation. With up to $180bn of new capital, there "should not be a realistic scenario" in which the government would be on the hook for losses even in a future financial crisis, Moelis claims. The government would nonetheless be paid a fee for providing a backstop against losses beyond that figure.
Details of the plan appear to be at odds with comments that Steven Mnuchin, Treasury secretary, has made about Fannie and Freddie. Last month he said he expected the pair to continue paying dividends to the government.
The document Moelis published on Thursday said the plan was "a clear and pragmatic path to achieve important public policy goals in a manner that will both protect taxpayers for years to come and respects the property rights of shareholders".