Shares in 888, which offers casino, poker and bingo games, were up 21 percent at 175 pence by 1459 GMT, with trading volumes nearly five times the stock's daily average. William Hill shares fell 3.5 percent to 376.2 pence.
"The company board confirms that it received an approach regarding a possible offer for the company by William Hill," 888 said. "There can be no certainty, however, that any firm offer will be made."
The Times report, citing industry sources, said talks could yet stumble because one of 888's Israeli founders, thought to be the Shaked family, wanted 300 pence per share. The company saw a 2011 planned takeover by Britain's Ladbrokes collapse over pricing.
Panmure Gordon analyst Karl Burns said that a deal at 210 pence was already quite pricey and that William Hill would be unlikely to raise its offer.
"I think there is a good chance that the deal may not go through ... it would stretch their (William Hill's) balance sheet to a degree that they may have to raise capital as well."
With tax and regulation increasing across the gambling sector's biggest markets, companies have begun to seek faster growth and more customers through online operations.
In November, online gambling company Bwin.Party said it was considering a range of proposals from interested parties. It has appointed Deutsche Bank to handle talks.