NEW YORK (CNN/Money) - The New York Stock Exchange is on the verge of announcing a radical new plan to allow large investors to trade big blocks of shares electronically on the floor of the exchange, according to a published report.

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The New York Times reported that the plan will be unveiled as early as Monday. It would be the largest change yet in the exchange's 212-year-old open outcry method of trading shares, which uses floor traders shouting orders to make trades.

The newspaper said the proposal has the support of NYSE CEO John Thain, who as the former chairman of Goldman Sachs supported his firm's move into electronic trading.

Thain has been charged with reforming NYSE in the wake of a trading abuse scandal involving the exchange's specialist traders, who have been accused of putting their own interests ahead of those of their customers.

Earlier this week, the NYSE and the Securities and Exchange Commission announced a settlement with two of the specialist firms, who agreed to pay $5.2 million in fines and restitution.

The NYSE has also been losing market share to aggressive new electronic trading exchanges. The plan to create a hybrid open outcry/electronic system is designed to stem those market-share losses.