In a statement today, LSE Group said that further to an announcement on 13 May, it had entered into exclusive discussions with The Northwestern Mutual Life Insurance Company, the US-based parent company of Russell.
LSE Group said: "Discussions remain on-going and there can be no certainty that a transaction will be forthcoming.
LSE Group says that a further announcement will be made in due course as appropriate.
Russell was founded in 1936 and has £160bn in assets under management. It is the creator of the Russell Global Indexes, including the Russell 2000® Index.
Russell provides a range of investment and asset management services to Financial Planners and advisers in the UK and US.
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In 2013 Russell announced it would acquire On-line Partnership Group Limited (OLPG) in the UK, expanding Russell's relationships with UK independent financial advisers.
OLPG has a network of over 600 advisers. At the time Russsell said: "Russell intends to expand the services provided by the OLPG's members, bringing new resources to bolster its existing investment research, technology and administration capabilities, as well as increasing training opportunities to help advisers thrive and better serve their clients in what is a new era for financial advice."