US fund manager Vanguard, which had about $1 trillion under management at the end of last year, is understood to have lodged an offer for UK-based Barclays’ iShares fund unit, the Sunday Telegraph said, citing unnamed sources.

Vanguard is being advised by William Blair & Company, a Chicago-based investment banking group, the newspaper said.

The offer from Vanguard underlines bidders' continued interest in iShares, despite Barclays' decision to begin talks with potential suitors for the whole of Barclays Global Investors, the operation within which iShares sits.

iShares is the world's largest brand in the fast-growing sector of exchange traded funds. ETFs, which are listed and traded like individual stocks, enable investors to get exposure to equity, bond and other market indices without the investor having to hold the underlying assets. Other large players in the ETF sector include Deutsche Bank and State Street. 

Under the terms of a deal struck in April to sell iShares to CVC Capital Partners, the private equity firm, for $4.4 billion (£3 billion), Barclays retained the right to find an alternative buyer for both that and "other related businesses". CVC has the right to match any subsequent offer accepted by Barclays, and will receive a sizeable break fee if the UK bank ultimately decides not to sell iShares to it.

A number of private equity groups, including BC Partners, have tabled rival proposals to buy iShares.

Barclays has until 18 June to solicit counter-offers.