Lloyds Banking Group's option of naming a deputy to ease the workload of Antonio Horta-Osorio, its chief executive on sick leave, risks adding to uncertainty over who will lead the bank, investors warned on Tuesday.

Lloyds, Britain's biggest retail bank, is considering strengthening support for Horta-Osorio to reduce the pressures associated with the top job, the Financial Times reported.

Options could include the appointment of a chief operating officer to act as an effective deputy or giving a small group of other senior executives increased responsibility, the FT said.

Investors said that Lloyds' various contingency plans over its CEO position were now at risk of adding even more uncertainty to an already difficult situation.

He's either CEO or not. They need to clear it up, said Brown Shipley fund manager John Smith.

Lloyds' finance director Tim Tookey is acting as caretaker CEO during Horta-Osorio's illness, but he is due to leave the bank in February.

Last week Lloyds named David Roberts as an interim CEO in case Horta-Osorio's return is delayed beyond Christmas.

If any company needs a clear line of management responsibility, it's Lloyds, Cheviot Asset Management partner David Miller said on Tuesday.

To try and go for a partial answer, while better than nothing, is still not satisfactory, added Miller, whose firm has a small holding of Lloyds shares.

Lloyds, which is 40 percent owned by the British government after a bailout during the 2008 credit crisis, shocked investors this month with news that 47-year-old Horta-Osorio was taking a break due to stress-related illness, leaving a potential power vacuum.

The bank reiterated on Tuesday that it expected Horta-Osorio to return to work before Christmas.

Antonio Lorenzo, who led Lloyds' strategic review, could become deputy to Horta-Osorio, the FT said, citing people close to the bank.

Given the upheaval, investors said they are unclear over who will lead Lloyds in 2012, when it faces major challenges from increased regulation, the economic downturn and plans to sell off 630 retail branches and cut 15,000 jobs.

There's still a lot of uncertainty over whether or not Horta-Osorio will come back, and whether to give him a deputy or not, said Royal London Asset Management fund manager Jane Coffey.

Lloyds shares were down 1.1 percent at 23.41 pence in morning trade -- still well below the average 63.1 pence price at which the British taxpayer acquired its stake in the bank.

The bank also said it was appointing George Culmer from insurer Royal & Sun Alliance as its new finance director. RSA said Culmer's leaving date was yet to be agreed.

(Additional reporting by Michelle Martin; Editing by Erica Billingham)