Sky Deutschland AG's supervisory and executive boards have advised shareholders not to accept a takeover offer by British Sky Broadcasting Group PLC, a week after the European Union approved the deal.

In a statement Wednesday, the board said the offer "doesn't reflect the long-term potential nor the internal value of Sky Deutschland."

Sky Deutschland also said that Chief Executive Officer Brian Sullivan, the only board member holding shares, wouldn't participate in the offer, which runs until Oct. 15.

In May, BSkyB said it planned to acquire Fox's 100% stake in the Italian TV company Sky Italia for GBP2.45 billion ($3.98 billion), with GBP2.09 billion of that in cash. The U.K. company also said it would buy 21st Century Fox's 57.4% stake in Sky Deutschland AG for GBP2.9 billion in cash, valuing the German business at GBP6.75 a share. At the time, BSkyB also offered GBP6.75 a share to Sky Deutschland's remaining minority shareholders, but BSkyB Chief Financial Officer Andrew Griffith said the company was "neutral" about buying out those holders.

21st Century Fox was until June 2013 part of the same company as News Corp, owner of The Wall Street Journal and Dow Jones Newswires.

Write to Monica Houston-Waesch at nikki.houston@wsj.com

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