The sell-off to private equity firms could be followed by the bank's entrance into the Asset Protection Scheme.
Barclays has attracted interest from industry big-hitters as it attempts to shore up its balance sheet through the sale of investment unit iShares.
A consortium of private equity houses are thought to be behind a serious bid for the business, the Sunday Times reports. Hellman & Friedman, Carlyle, TPG and Apax are said to be the four firms involved.
Hellman & Friedman already has some experience in running an asset management business, through its acquisition of UK-based Gartmore. In total, the bid is thought to be worth around £3.5 billion.
iShares is known among private investors for its extensive range of exchange-traded funds (ETFs). A comparatively recent innovation, ETFs work as a fund which is bought and sold on a stock exchange - and generally track the value of indices such as the FTSE 100.
With the markets having retreated by around 50 percent since the onset of the credit crunch, index trackers could potentially enjoy a surge in popularity thanks to an influx of bottom-fishing investors.
Barclays itself has been seeking an infusion of fresh capital due to its balance sheet troubles caused by the continuing credit crunch. The bank negotiated a £5 billion investment from the Abu Dhabi royal family last year, due to the difficult conditions.
However, Barclays recently confirmed that it was in talks with the Treasury over its participation in the Asset Protection Scheme, which sees the government offer insurance for toxic assets held by banks. Entering the scheme would represent the first time the previously independent bank has accepted assistance from public money in the crisis.
The possibility of Barclays taking a more drastic step and being part-nationalised through selling off an equity stake to the government, in a deal similar to those undergone by RBS and the Lloyds Banking Group, also remains open.
