According to reports in The Sunday Telegraph, an unnamed L&G executive said: "We have written to the company to say that we are planning to vote against."
Sky is proposing a buy-back of of 5% of its shares, a move that would increase the stake of major shareholder News Corp to 39% from 37%.
The buy-back will be among the resolutions put to shareholders at BSkyB's November 4 annual meeting.
News Corp needs approval from Sky shareholders to take part in the buy-back because its shareholding is above 29.9% and any increase would trigger an automatic bid for the company due to Takeover Code rules.
BSkyB UK shareholders have demanded a statement from the satellite broadcaster or News Corp that the voting stake will not be increased beyond its 37% cap.
L&G, which holds a 2.5% stake in BSkyB, was not immediately available for comment.
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