Bloomberg - having spoken to four people who are familiar with the talks and wished to remain anonymous - reports that the sale of the British taxpayer's Â£65.8 billon ($107 billion) portion in the institutes is likely to go ahead next year.
After rescuing both groups during the economic downturn, the government owned more than 80 per cent in RBS and a significant minority in Lloyds.
The insiders suggested Lloyds is likely to be offered to investors first, as it is better prepared for a sale.
Three of the four questioned said the coalition will attempt to return RBS back to a majority private ownership before 2014 draws to a close.
Professor of politics at Bristol University Mark Wickham-Jones commented: "That level of windfall would open the way for tax cuts in the run up to the next election ... that could be a remarkable opportunity for the coalition."
The news outlet noted the Conservative-Liberal Democrat coalition will have the freedom to spend privatization proceeds on various areas as the country's budget deficit will have reduced by more than two-thirds by 2015.
And Stephen Driver, author of Understanding British Political Parties, observed: "If you're a Conservative government wanting to make sure you mobilize the Conservative vote, how better to do that than through tax cuts?"
The news comes shortly after Bloomberg reported that employment in the UK's banks is escalating back up to levels almost as high as was recorded before the economic downturn took hold.
It was shown that Goldman Sachs Group currently employs almost as many people in London as it did in 2007, while RBS has more workers in its securities unit than it had four years ago.
By Tony Aynsley