Lloyds, which must sell the business as a condition of its government bailout during the financial crisis, said the shares would be sold at between 220 pence and 290 pence each.
The mid-point of the range values the business at 1.28 billion pounds ($2.1 billion), below its book, or net asset value, of 1.6 billion pounds.
The price reflects a cooling of investor interest in UK company flotations in recent weeks following a rush of activity earlier in 2014. Clothing chain Fat Face pulled its planned London listing last week while shares in insurance-to-holidays firm Saga have fallen below their IPO price.
Lloyds, 25 percent-owned by the government, is obliged by European competition regulators to sell the 631 branches which now form TSB as a condition of receiving state aid during the financial crisis five years ago.
It must sell the whole of TSB by the end of 2015 and banking industry sources expect it to carried out in three or four tranches. TSB will publish the prospectus for the initial public offering later on Monday. Final pricing will be announced on June 20, with initial dealings starting on the same day.
TSB has 4.5 million customers and 6 percent of bank branches in the UK, making it Britain's seventh-largest retail bank and giving it a head start over other challenger banks.