Lloyds Banking Group expects to launch a stock market float of the revived TSB business, which employs more than 1,000 people in the county, within eight weeks.
The offering will include a retail element for private shareholders.
Lloyds, which is still 25 per cent owned by the taxpayer, also revealed yesterday that its underlying profits rose by 22 per cent to £1.8 billion in the first quarter of 2014.
Lloyds Banking 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. It has 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."
Mr 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."
Meanwhile, TSB announced at the end of last year it was recruiting 104 more people at its offices in Barnwood, one of the bank's key UK centres. They added to the 950 staff it already employed there.
A further nine posts in customer assistant and personal banker roles were created at the bank's branches throughout Gloucestershire.
These include Quedgeley, Cirencester, Dursley, Gloucester, Stroud, Tewkesbury, Hucclecote, Wotton-under-Edge and Ross-on-Wye.