Private equity groups Hellman & Friedman, Bain Capital and TPG
Talks with a consortium around Hellman & Friedman were moving quickly and smoothly, one of the sources said. It was not immediately clear who else was in the consortium.
Barclays, which said on Monday it may sell the iShares exchange-traded funds provider, declined to comment.
Another source familiar with the situation that said Bain Capital was interested in iShares, while a third source said that TPG was also looking at the unit.
Analysts have put the value of iShares -- part of Barclays Global Investors, the San Francisco fund management arm -- at around $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
(Additional reporting by Steve Slater, Writing by Douwe Miedema)