The bank's advisers sounded out investors about a potential rights issue last week as it looks for ways of meeting the Bank of England's demands that it raise capital levels, The Sunday Times reported.
The bank is struggling to meet a new rule imposed by the Bank's Prudential Regulation Authority (PRA), which demands it holds more assets as a buffer against future financial crises.
The PRA recently ordered Britain's five biggest lenders to raise another £13.4 billion to plug a higher-than-expected £27.1 billion hole in their finances - including ordering Barclays to raise £1.7 billion.
The PRA also imposed a new rule, called the leverage ratio, demanding big banks must hold capital worth 3% of their loans.
Barclays was told it has a leverage ratio of 2.5% - prompting speculation the Bank has rushed forward the deadline for meeting this rule from a previous deadline of near the end of this decade.
Chief executive Antony Jenkins has criticised the measure as "crude" and said it would hit the target by 2015, adding any move to speed up this process could force it to squeeze lending. The PRA has rejected anything that restricts lending - preventing Barclays from shrinking its loan book to meet the target.
Barclays will announce plans for meeting the tougher rules on Tuesday when it publishes half-year results.
The bank's results are also predicted to show bigger-than-expected provisions to account for previous mis-selling of interest rate swaps, payment protection insurance (PPI) and identity fraud protection.