Caesars Entertainment, the Las Vegas casino-owner, says it is in advanced takeover talks with William Hill over a possible £2.9bn bid for the bookmaker.
The US firm said William Hill's board had indicated it is minded to recommend its cash offer of 272p a share.
William Hill has also received a takeover approach from US private equity firm Apollo.
But Caesars said if William Hill chose Apollo, it would jeopardise a joint venture between the companies.
Caesars owns a 20% stake in William Hill's US operations, which also have exclusive rights to operate sports betting under the Caesars brand.
The US firm, which owns Caesar's Palace in Las Vegas, is particularly interested in William Hill's US bookmaking business which currently has 170 retail sites in 13 different states.
Caesars chief executive Tom Reeg said: "The opportunity to combine our land based-casinos, sports betting and online gaming in the US is a truly exciting prospect.
"William Hill's sports betting expertise will complement Caesars' current offering, enabling the combined group to better serve our customers in the fast growing US sports betting and online market."
On Friday, William Hill confirmed that it had received two takeover approaches, which sent its share price soaring by 42% to 312p.
Caesars said its offer was nearly 58% higher than William Hill's share price on the day before the US company made its first approach on 2 September.
It added it was also above the betting company's share price on Thursday last week, before its disclosure of the two approaches caused its share price to surge.
But David Cumming, chief investment officer for equities at Aviva Investors, said offers for William Hill could outstrip the 312p level its shares ended at on Friday.
He told the BBC's Today programme: "The view is - and we do hold some William Hill so it [has] some interest here - the 40% rise on Friday, given comparative valuations in the US, it is possible that the bid comes in at a higher level than the closing price we saw then so there still might be some upside."
Apollo - which is also one of two firms in the final running to buy UK supermarket Asda - is yet to publish details of its possible offer for William Hill.
However, Mr Cumming said he thought Caesars was the most likely victor "because it already owns 20% of William Hill's US business and so it should have some synergies".