It said that as a result of the discussions Crystal Amber is looking at building its own position worth tens of millions of pounds in Sainsbury's so it can participate in any major shake-up of the grocer.
The Sunday Telegraph said Crystal Amber believes a club of activists would be able to either flush out a bid for Sainsbury's from another large international retailer or force it into a major sell-off of its property estate.
It said Crystal Amber doesn't have the firepower to engineer any real change at Sainsbury's on its own.
No one at Crystal Amber was immediately available for comment, while a spokesman for Sainsbury's declined to comment.
Crystal Amber does not show Sainsbury's as being one of its current investments, according to its monthly statement on top-ten holdings.
It had assets under management of 118 million pounds as of the end of September, and a net asset value of 150.1 pence a share at the end of November. The shares last traded on London's junior AIM market at 148.1 pence on Friday, valuing the firm at 112 million pounds.
Sainsbury's shares, which have lost 35 percent of their value so far this year, closed on Friday at 239 pence, valuing the business at 4.6 billion pounds.
Sector analysts gave little credence to the report.
"It's a bull-market story when it's painfully clear that supermarkets are in a bear-market," said independent retail analyst Nick Bubb.
He added that separating the value of freehold property from the value of the trading assets was no longer feasible, with the value of supermarket freeholds under threat and trading profitability eroding quickly.
Last month Sainsbury's said it planned to cut costs, dividends and new store openings to fund 150 million pounds of additional price cuts, partly to counter the growing threat of German discounters Aldi and Lidl to traditional grocers.
Some 26 percent of Sainsbury's equity is owned by the Qatar Investment Authority, which walked away from a possible takeover in 2007, while the different parts of the Sainsbury family own around 11 percent.