The retail entrepreneur, who also owns the Arcadia fashion chain, is quoted in a British Sunday paper as saying he would not be making a bid after studying financial information on Safeway.
The report adds another twist to a long-running takeover saga as Trade and Industry Secretary Patricia Hewitt prepares her response to a Competition Commission inquiry into the four supermarket chains currently circling Safeway.
Mr Green is the only one of five interested parties to have been given the all-clear by regulators. The announcement from Ms Hewitt, which is expected later this week, is likely to offer a clear path to Morrisons with Wal-Mart-owned Asda faced, at best, with the prospect of selling off a large number of stores.
Tesco and Sainsbury's are set to be blocked as the Commission tackles concerns that a dominant supermarket group would damage shoppers and suppliers.
The only condition likely to be imposed on Bradford-based Morrisons is that it sells around 50 of Safeway's 480 stores in areas where the two chains overlap.
That could still prompt chief executive Sir Ken Morrison to lower the price that Morrisons offers for Safeway after tabling a stg£2.9 billion offer in January. Should Asda now Britain's second largest supermarket chain be blocked, it is thought the company may be prepared to link up with a private equity bidder in order to acquire a tranche of stores.
It has also been reported that Safeway's own management team may put together its own proposal if bid values fail to come up to scratch. Such a move is also likely to involve the sale of a number of stores.
Prior to yesterday's reports, Morrison was 2/1 favourite with City bookies Cantor Index to land Safeway the UK's fourth biggest supermarket chain with Philip Green second at 7/2 and Asda third at 4/1.