Fasano's bill would eliminate advance collections; a Democratic lawmaker filed a similar proposal.
"A lot of people are paying for something that they'll never see any return on their money," Fasano said.
The fees have also been targeted in court, but the Florida Supreme Court has not yet ruled on whether to overturn them.
Southern Co. also benefits from advanced collections, though Georgia lawmakers have not focused on that money.
The Florida Public Service Commission voted in November to allow the state's two largest utilities to charge customers for $294 million this year for the costs of future nuclear facilities.
Progress Energy Florida, which has been purchased by North Carolina-based Duke Energy, has collected more than $819 million from its customers for two nuclear projects, according to the Florida Public Service Commission.
One was to expand the capacity of the now-crippled Crystal River plant, work that resulted in damage that shut down the facility.
The utility was also using the fee to pursue a new nuclear plant in Levy County.
Progress Energy Florida still needs a license for the plant from federal regulators and pushed back the opening of the first Levy County reactor to 2024. Some question whether it will be built at all.
Four GOP senators in Florida said recently they will seek to put limits on the collections. Lawmakers said their upcoming bill will set a deadline for utilities to start construction and make sure power companies cannot earn a profit off any prepayments if they do not build a nuclear facility.
"On the details, there is plenty of room for conversation," Sen. John Legg said at a Feb. 21 news conference. "But on these three principles there will be no room for compromise."