The step would leave the way open for Jerome Seydoux, chairman of the French media group Pathe and currently a non-executive director, to take over the position.
Mr Robinson, who has held the post since December 1994, has recently taken on the job of chairman of the Arts Council. But industry insiders dismissed the suggestion that Mr Robinson, who prides himself on his short working hours, was seeking to reduce his workload.
The news comes amid signs of mounting tension between BSkyB and British Digital Broadcasting (BDB), the digital broadcaster in which Granada has a 50 per cent stake.
Last month, it emerged that BSkyB had issued a writ against Granada and Carlton, the other shareholder in BDB, after the two groups stalled on a pounds 70m payment. BSkyB is also involved in a stand-off with the Premier League about extending its rights to show live football matches to BDB.
Mr Robinson is likely to be quizzed about his position on Tuesday, when BSkyB reveals its interim results. Analysts expect pre-tax profits to fall to between pounds 123m and pounds 140m due to the rising cost of sports rights and the costs of launching digital satellite television, scheduled for June.