The Conservative Party has pledged to do this if it wins the UK's general election on May 7. Moreover, the UK lender's solid first-quarter results may have reinforced Chancellor George Osborne's thinking.
Losses from bad debts dropped 59 percent from a year ago, and fresh charges for retail insurance misselling were avoided.
Lloyds' net interest margin, the difference between the interest it receives and pays out, and thus an indicator of future revenue, rose strongly.
The outlook for dividends is promising too.
Lloyds' common equity Tier 1 ratio grew to 13.4 percent at the end of March, well ahead of its 12 percent target. Legal costs and regulation could well bring that down, but on current terms and factoring in, say, another 800 million pounds in new PPI provisions, it represents up to 3.5 pence per share, on Breakingviews' calculations.
It is hardly surprising that Lloyds is thriving. UK unemployment and interest rates are low, easing pressure on debt repayments. Losses on UK banks' loan books last year were at a 25-year low of 0.14 percent, according to Standard & Poor's.
But banks are leveraged, cyclical entities better suited to ownership by institutional rather than retail investors.
For one thing, institutions have readier access to capital to support crisis-hit banks.
And Lloyds' recent strength makes a series of institutional share sales easier.
On the blistering pace set in March and April, the state could be shot of its remaining 20.95 percent holding within 12 months.
That would be less risky than delaying to tick all the boxes necessary for a retail offer.
Proponents of a retail offer say taxpayers ought to share in any potential upside.
But the UK citizens that might be interested in adding Lloyds to their portfolios may already own its shares via pension schemes and other collective savings products.
Besides, there is a danger too many retail shareholders will assume Lloyds is on a one-way path to growth.
Rather than running the risks of a retail offer, offloading a dividend-paying Lloyds quickly, before the credit cycle turns, would be a better way to reward the UK taxpayer.