This weekend, sources said that private equity groups Hellman & Friedman, Bain Capital and TPG
H&F wanted to form a consortium and was eyeing an offer of around $5 billion, while Bain Capital and Goldman were mulling separate offers, the first source said on Monday.
Bids for the business are not due until at least this Thursday, the person said.
Separately, the Financial Times reported on its website that other trade bidders that are thought to be interested in iShares include Vanguard, the U.S. fund manager specializing in index-tracking funds.
Barclays, which said last week it may sell the iShares exchange-traded funds provider, declined to comment.
Analysts have put the value of iShares -- part of Barclays Global Investors, the San Francisco-based fund management arm -- at around 3 billion pounds ($4.37 billion), more than one-third of Barclays's market capitalization.
The Wall Street journal reported on Friday that Barclays was offering to finance the purchase of the unit, lending up to 80 percent of the unit's price.
Barclays Capital, the investment bank, is one of the biggest providers of funding for buyouts, but like all banks it has pulled back on providing buyout loans during the crisis.
It might be more willing to provide a big loan for a business it knows so well, however, especially if it helps its parent achieve a deal to secure much-needed cash.
Barclays could use the proceeds of any disposal to cover the cost of joining a government scheme to insure banks against losses on risky assets.
A sale could also remove the need for the bank to sell new shares, or issue them directly to the state.
That would enable Barclays to avoid surrendering a stake to the government, in contrast to other British banks such as Royal Bank of Scotland
(Reporting by Victoria Howley; Writing by Douwe Miedema; Editing by Gary Hill)