City sources said Wimpey had made a bid for Banner, a private company, and was expected to approach Laing Homes. Sources said Wimpey had the money to make the double bid, even though it bought McAlpine Homes for £461m last year.
Wimpey refused to comment, and would not be drawn on any acquisition plans when quizzed by analysts.
City pressure on housebuilders to consolidate has intensified after Taylor Woodrow, Persimmon and Wimpey acquired Bryant, Beazer and McAlpine respectively. Smaller deals have included Westbury's purchase of Prowting and Wilson Connolly's acquisition of Wainhomes.
Bovis Homes, Redrow and Barratt are also thought to be on the lookout for possible deals.
Laing is likely to be sold for about £300m, whereas Banner, which is much smaller, would be worth no more than £50m. An analyst said: "Wimpey is my favourite to get Laing and it could well manage Banner too. They are both good fits."
But another City source questioned whether making two acquisitions so close together was wise. He said: "Another deal for Wimpey right now would not go down well. The market wants to see if it can absorb what it already has. People will be watching what Peter Johnson, the chief executive, does very closely."
Wimpey is likely to face stiff competition for Laing from a management team led by managing director Steve Lidgate. Building has learned that venture capitalist 3i has decided to back the management team despite earlier concerns that a buyout was not the best option for Laing's housing business. Persimmon had also been tipped to bid for Banner Homes, but it now appears that it will not do so.
Wimpey said in a trading statement on Wednesday that UK completions had risen 27% for the first six months of the year compared with the same period last year.
It reported that average selling prices had jumped 18% to £139,500. Johnson said the housing market was still healthy.