Westbury and Wimpey have been touted as possible stalkers as the wave of consolidation in the industry continues. Swan Hill is seen as an attractive and well-performing company in the higher end of the market. Its average selling price is £194,000.
Linden's sale follows frenetic activity two weeks ago, when 3.7 million shares were traded in a single day but which Swan Hill dismissed as trading between institutional investors.
Linden chief executive Philip Davies could not be reached for comment this week.
Swan Hill's share price has jumped 12p (14%) to 89p since the stock activity started.
Analyst Leslie Kent of Seymour Pierce said the recent interest was unprecedented for the small, west London-based housebuilder, which last year completed 208 houses.
He said: "It's a real mystery but someone will have to put their hand up soon. If someone was wanting to go upmarket, you could do a lot worse than Swan Hill." Kent predicted the buyer would announce an offer for Swan Hill at the same time as it announced its holding.
But Swan Hill again downplayed the activity. Chief executive John Theakston said he was confident his company was not the target of a takeover bid.
He said: "It wasn't a predator. I am very confident that the shares have gone to an institutional investor." Theakston declined to name the investor in question.
He said the activity was more likely the result of institutional investors liking the reorganisation of the company that has seen it move from property and construction to housebuilding. He said: "Investors have been watching to see if we were successful and we have been." Swan Hill has a landbank of 680 plots in the south of England and a net asset value per share of 125p. This means that the company is still substantially undervalued on the stock market, despite the recent rise in the share price. Kent said Swan Hill's market capitalisation was £53m but any bidder would have to pay about £70m for the company, which posted pre-tax profit of £2.3m on turnover of £58.6m last year.