* Buyers found for maximum 33 pct stake -source
* Buyers' offers within 160-195 pence price range -sources
* Book fully covered 3 days into 9 day roadshow -sources
(Adds stake fully covered, analyst comment)
By Matt Scuffham and Myles Neligan
LONDON, Oct 3 (Reuters) - Royal Bank of Scotland has found buyers for the full 33 percent stake of insurer Direct Line it is selling to stock market investors, just three days into a nine-day marketing drive, sources close to the transaction said.
RBS is selling Direct Line, Britain's biggest motor insurer, to win European Union regulatory approval for a government bailout it received during the 2008 financial crisis that left it 82 percent state-owned.
"The book is now fully covered within the range, and to get that done three days in is pretty encouraging," one of the sources said, referring to the price range of 160-195 pence set last week.
Direct Line would be worth 2.66 billion pounds ($4.29 billion) at the mid-point of the price range, at the lower end of the 2.5 billion pound to 3.5 billion pound range of market forecasts.
The price range reflects volatile financial markets that have derailed some planned European flotations this year.
The initial public offering, London's biggest in a year, has faced further pressure because of investor worries about weak growth prospects in the British motor insurance industry, which is also facing an anti-trust probe.
"The headwinds from the current softening pricing environment, macro challenges to the home and commercial market, and margin pressure from regulatory changes ... will be too much," Espirito Santo analyst Joy Ferneyhough wrote in a note on Wednesday, valuing the company at 2.4 billion pounds.
Another source said banks handling the sale had so far focused on attracting British investors, and would now turn to marketing the shares in North America and continental Europe.
RBS said last month it would sell a maximum of 33 percent in Direct Line in the first of several share offerings aimed at disposing of the business entirely by the end of 2014.
If priced at 195 pence, the insurer could raise as much as 975 million pounds, making the sale London's biggest initial public offering in over a year. Order books, which opened on Sept. 28, are due to close on Oct. 10.
British spread betting firm ETX Capital was on Wednesday quoting a spread of 179 pence to 189 pence on Direct Line shares, up from 177 pence to 187 pence on Tuesday, reflecting investor expectations of a higher offer price.
The spread gives investors the opportunity to bet the stock will rise above 189 pence or fall below 179 pence when it starts trading.
Edinburgh-based RBS has been under political pressure to secure a good price for Direct Line to help reduce the British taxpayer's current loss of 22 billion pounds on the 45 billion pounds the government pumped into the bank to secure its future.
The shares are being offered to retail investors as well as institutions. On Monday, stockbrokers involved in the listing reported good interest from private investors.
Goldman Sachs and Morgan Stanley are running the offering, and are joint bookrunners with UBS . RBS and Direct Line declined to comment. ($1 = 0.6196 British pounds)
(Additional reporting by Steve Slater; Editing by Catherine Evans)
Keywords: DIRECTLINE IPO/