The bookie described the proposal, which valued William Hill's stock at 364p per share, as "complex", "highly opportunistic" and a substantial undervaluation of the company.
It proposed a merger of Rank and 888 to create a new company called BidCo, which would then contemporaneously take over William Hill in a mixed offer for cash and shares in the new entity.
The consortium claimed it had identified £100m in annual cost savings from the tie-up and increased marketing effectiveness.
"Everything William Hill needs, we have on steroids," 888 chief executive Itai Frieberger told City A.M. on Thursday.
Rank and 888 are widely expected to launch a revised offer before 21 August. Last Thursday, the companies said they would still "welcome the opportunity to engage" with the bookie's board of directors to negotiate a new version of the deal.
The ailing bookmaker has been perceived by many as a takeover target as it has battled to break into the online betting market but has been losing ground to rivals.
Rank and 888 declined to comment.