The French media giant has made inquiries to investment bankers about its options for the stake, which is valued at £3bn. A sale to institutional investors could reduce the power of News Corporation chairman Rupert Murdoch at the broadcaster, according to reports.
Vivendi holds one seat on the broadcaster's board and a sale of Vivendi's stake to institutional investors would likely force a series of changes at board level. Murdoch's News Corp, with a 37% holding, is the satellite TV broadcaster's largest shareholder.
Vivendi is said to be considering a contingency plan if it cannot negotiate an asset-swapping deal with BSkyB. Earlier reports suggested that Vivendi might exchange its BSkyB stake for a minority shareholding in USA Networks, which belongs to US cable magnate John Malone.
Some bankers are said to have advised Vivendi that it would get a better price for its stake on the market than from a sale to a strategic investor, which would have to be satisfied with remaining a minority shareholder in BSkyB.
BSkyB shares were trading at 700p at 11.20am -- it had fallen the furthest of the blue-chip stocks in the FTSE 100 this morning, despite reassurances from the French media giant that it had no plans to seek a stock market placing for the holding.
Late last year, Vivendi agreed to give up the stake within two years in return for EU regulatory approval of its $34bn (£24bn) takeover of Seagram, the Canadian group which owned content giants Universal Studios and Universal Music.