The legal battle is over a portion of Cuba's unpaid commercial debt dating back to the 1980s.
If they don't reach a deal, Cuba could then face yet another court fight over whether it finally has to pay.
Because of the U.S. embargo against Cuba, American investors are prohibited from owning and trading Cuban debt, which frustrates some frontier-market hedge fund managers in the U.S.
They argue that holding Cuban debt would better serve U.S. foreign policy interests because it would give Americans a seat at some future negotiating table.
CRF, meanwhile, says in court filings that it first reached out to Cuba 10 years ago to settle the debt but were ignored.