Scandal-hit RBS - which is 81% state-owned after a £45 billion bailout in 2008 - could be ready for privatisation this year, but at present prices that would mean a huge public loss.
The Liberal Democrats have championed the idea of a share giveaway and it was reported today that Conservative ministers were also now examining the idea of handing it back to taxpayers.
Party sources told the Independent and Daily Mail that Chancellor George Osborne saw continued ownership as politically "untenable" amid Libor-fixing and other scandals and was keen to end the state's role soon.
They told the newspapers Economic Secretary to the Treasury Sajid Javid had been tasked with drawing up options and that giving everyone in the country shares worth £300-£400 would be a vote winner and stimulate the economy.
"One of the options of course could be to put it in our manifesto - but then Labour could do that as well," they were quoted as saying.
"Wouldn't it be much better if voters were getting a cheque for £400 a few months before election day? It would also be a very big stimulus."
Short of a giveaway, some shares could be offered to the public at a discount.
The Treasury insisted that no decisions had been taken and that its aim remained to return RBS to the private sector "at the appropriate moment" and with the best possible outcome for the taxpayer.
Business Secretary Vince Cable said earlier this month that while there was "no immediate prospect" of a giveaway, "my party has advocated that option and we want to keep that option alive".