L&G has made an approach for Cofunds, in which it has a 25% stake, in a deal which could value the supermarket at up to £200m, according to reports.
The Sunday Telegraph reports that Mark Gregory, L&G's group executive director of savings, approached Charlie Eppinger, Cofunds' chairman, with a written expression of interest last month.
The insurer's executive management team, led by outgoing chief executive Tim Breedon, is understood to want to build out its fund platform, according to the paper.
However, the offer could be usurped following early-stage interest from private equity house Bridgepoint, which is understood to want to speak to Cofunds' board.
In addition to L&G's stake, IFDS owns 24% of Cofunds, US investor Newhouse Capital has 18%, while Threadneedle and Jupiter own 20% and 10% respectively, and Prudential holds 3%.
Although better known for its consumer investments, including Fat Face, Hobbycraft and Pret A Manger, Bridgepoint does have a history of involvement in UK financial services.
It made a considerable return on Tilney, the wealth manager which it sold to Deutsche Bank for £350m in late 2006, 18 months after buying it for approximately £100m, the Sunday Telegraph reports.
It is understood L&G is yet to receive a formal response from Cofunds, and it is not known if other shareholders are aware of the approach.
An L&G spokesman declined to comment.
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