Discussions between the companies were “relatively advanced” and an announcement could be made on Monday, the newspaper said, citing sources.
A tie-up between the two groups would be the latest in a string of major deals in an industry consolidating in the face of tighter regulations and rising taxes.
British bookmakers Ladbrokes LAD.L and Gala Coral are awaiting clearance for 2.3 billion pound deal, while Paddy Power PPB.I and Betfair agreed to join forces in September.
888 had agreed to buy UK-listed Bwin.party last year, but it was jilted in favor of a higher offer from GVC Holdings (GVC.L).
A spokesman for Rank declined to comment. 888 did not immediately respond to a request for comment.
($1 = 0.7628 pounds)
Reporting by Paul Sandle; Editing by Raissa Kasolowsky