The offering will include a retail element for private shareholders.
Lloyds, which is still 25% owned by the taxpayer, also revealed today that its underlying profits rose by 22% to £1.8 billion in the first quarter of 2014.
The group - rescued by the government at the height of the financial crisis - was ordered to spin off more than 600 branches under EU rules on state aid, and has already rebranded the sites as TSB after the collapse of a deal to sell them to the Co-op.
Chief executive Antonio Horta-Osorio said: "Following the launch of TSB Bank in the second half of 2013, we have continued to prepare for an IPO (initial public offering) of the TSB business.
"We are now well placed, subject to final regulatory approval and market conditions, to launch the IPO in the summer of this year."
Horta-Osorio added that Lloyds will be selling a minimum of 25% of the business in the offering. Finance director George Culmer said: "We would be hopeful that there would be an announcement ahead of the end of June.
"There will be a retail element. The final details in terms of issuance and allocation are still to be decided."
Lloyds said it was in a strong position ahead of talks with the Prudential Regulation Authority in the second half of this year to restart dividend payments which could see a full-year reward for shareholders in May 2015.
Culmer said: "I would go into those discussions with confidence about our business and about our prospects."
Lloyds also said it had not needed to add to the billions of pounds put by to cover compensation for customers who were mis-sold payment protection insurance (PPI).
It still has £2.3 billion kept aside to deal with continuing claims though Culmer was cautious when asked if this would be enough to see the bank through the scandal, which has crippled its balance sheet in recent years.
"I am never going to say never on PPI," he said. Lloyds expects to have completed sending out letters to customers it believes might have been affected by the middle of the year.
Reported profit before tax fell 33% to £1.4 billion compared with the same period last year, with the comparison including the impact of its sale of a stake in asset manager St James's Place.
Lloyds said it lent £2.6 billion to first-time homebuyers in the first quarter, including £342 million through the Government's Help to Buy scheme. Loans to small and medium businesses grew by 5% in the last 12 months, it added.
Horta-Osorio said: "We improved the service we deliver and the products we offer, and are helping Britain prosper.
"The group delivered successfully in the first quarter, and we are well positioned to make further progress in the remainder of 2014."
In March, the government reduced its stake in Lloyds to 25% after a £4.2 billion placing of shares with institutional investors. It further cut the Treasury's holding after a £3.2 billion placing last September.
A further multibillion shares offering to members of the public is expected later this year.
When asked about when he would like to see the remainder of the taxpayer stake returned to private hands, Mr Horta-Osorio said: "We don't have a preference about this." He said the bank would seek to co-operate with the Treasury's wishes. Shares rose by nearly 4%.
Richard Hunter, head of equities at Hargreaves Lansdown stockbrokers, said: "Lloyds is often seen as a proxy for the UK economy, and although they are inextricably linked, both are beginning to prosper after a long period of austerity.
"Outlook comments are also upbeat, but not excessive given the fact that there remains some way to go.
"Less positively, the Government stake remains an unwelcome influence, the stock cannot yet appeal to income seeking investors and the possibility of further regulatory censure weighs heavily on the sector."