Sources close to the negotiations say Italian banks such as San Paolo di Torino, or the Spanish heavyweight Argentaria, are among those being touted as possible buyers, as well as the usual crop of German and French banks.
Phoenix Securities, which is advising Lloyds, is understood to be well advanced in marketing the business to European financial institutions. However, analysts believe Lloyds faces an uphill struggle to achieve a quick sale.
TSB itself tried to sell Hill Samuel some four years ago but was unable to find a buyer. The merchant bank has now made a significant recovery from the poor lending policies and ruinous bad debts in the recession. But the City also believes buyers for the whole of Hill Samuel will be hard to find, and the price may not be much more than pounds 100m, a fraction of what TSB paid in its ill-fated takeover of the bank during the stock market crash of 1987.
"It has already marketed the business around Europe one time. It will find it harder this time around," one analyst said.
Once one of the finest City names, Hill Samuel no longer boasts the corporate client base that attracted buyers prepared to pay premium prices for names such as SG Warburg, sold to Swiss Bank Corp, or Barings, where Dutch Bank ING stepped in despite the debacle of rogue trader Nick Leeson's losses.
Lloyds' success has been firmly based in its clearing bank business, and Hill Samuel staff have already experienced a clash of cultures with Lloyds' traditional high-street banking ethos.
Hill Samuel points out it has been rebuilding its corporate finance operations, and Hugh Freedberg, its chief executive, has been credited with restoring some pride to the bank. Recent high-profile deals include its role as adviser to the Government on the Channel Tunnel rail link.
The price depends on what is sold. Hill Samuel's total profits were restored to pounds 64m in 1995 and net assets stood at pounds 420.6m in October 1994. But Lloyds may retain a large proportion of Hill Samuel's corporate loan book and clients.