Paragon yesterday said it was in exclusive talks to buy the business, which offers funding to property developers and solicitors, from the National Counties Building Society.
The purchase would enable Paragon to gain a banking licence and start offering savings accounts to customers.
In a statement to the markets, Paragon said it was in the “early stages of considering the acquisition of Hampshire Trust”.
“There is no certainty that a transaction will be concluded,” it added.
The deal would allow Paragon to offer other retail products such as savings bonds, which would give it an alternative source of funding.
Paragon, which is listed on the FTSE 250, has performed strongly during the economic downturn with buy-to-let mortgages in demand as landlords take advantage of a booming rental market while first-time home buyers struggle to get on the housing ladder.
The West Midlands based company has expanded through acquisitions as mainstream lenders sell off loans.
Shares in Paragon Group, which has around £9.6bn of loan assets under management closed up 0.75 per cent.