The board of Lloyds Banking Group is expected to decide this week whether chief executive Antonio Horta-Osorio is fit enough to return to work.
The Portuguese banker, who was signed off work last month with exhaustion, has already had one-to-one meetings with some non-executive directors about continuing in his post.
More discussions are set to take place this week before Thursday's board meeting, when a decision on Mr Horta-Osorio's future may be made, the Sunday Times said.
UK Financial Investments, which manages the Treasury's 41% stake in Lloyds, is also understood to have told the bank it is happy for him to carry on.
Thursday's board meeting is also likely to see a decision on competing bids for Lloyds' Project Verde branch network from buyout vehicle NBNK and the Co-operative. Both bids are thought to be in the region of £1.5 billion, although Lloyds has not ruled out a stock market flotation.
NBNK Investments, which is a takeover vehicle run by former Northern Rock boss Gary Hoffman, is thought to be slight favourite to secure the 632 branches, which are being sold in order for Lloyds to meet European competition rules.
Press Association, photo by The CBI