* Greece preparing sale of seven-year bonds
* Economy showing signs of improvement
* Greece hoping to attract conservative bond investors
* Many still worried about high debt levels
* Hedge funds attracted by exciting returns
LONDON, Feb 1 (Reuters) - Greece's economy is growing, its credit ratings are on the up, the government has returned to bond markets and hopes to leave the 86 billion euros bailout that kept it from default.
But it will still be a challenge to lure long-term investors to an imminent sale of seven-year bonds.
Greece returned to the bond markets last year for the first time since 2014. The 3 billion euros sale of five-year bonds was deemed a success with a yield of 4.625 percent.
That sale was heavily supported by hedge funds. It would be a sign of confidence if Greece can attract a higher proportion of conservative funds, in it for the longer haul, at the new debt issue which could come as early as next week.
Two big bond investors told Reuters they were unlikely to take part in upcoming Greek bond sales because they were still concerned about the sustainability of Greece's debt. Another said he would approach it with caution.
Greece has had three bailouts in the last decade and a debt-to-gross domestic product(GDP) ratio approaching 200 percent, the highest in the 28 member European Union.
"Greece is a controversial story because on one hand, the economic picture is better and reforms asked for by the European Commission were voted through, whereas on the other hand, the total amount of debt is still there," said Patrick Barbe, head of European bonds at BNP Paribas Asset Management.
His European sovereign and aggregate bond team has no exposure to Greece as its low credit rating puts the country below the threshold that would allow the firm to invest there.
He said he was cautious about buying upcoming Greek bond issues.
S&P last month lifted Greece's rating for the first time in two years but at 'B,' Greece remains five notches below the "investment grade" threshold that would open it up to a much wider pool of investors.
Its rating also puts Greece on par with Nigeria, Rwanda, Cape Verde and a notch below serial defaulter Argentina.
Other numbers are pointing in the right direction. Economic growth is running at 1.3 percent on an annual basis and data on Thursday showed factory activity expanding at decade-highs and a record pace of job creation.
Seamus Mac Gorain, senior fixed income portfolio manager at JPMorgan Asset Management, which manages assets of $1.6 trillion, said although the strong growth environment means more confidence in high-yield borrowers such as Greece, debt levels would be a "headwind" for a move to lower borrowing costs.
Greece's relatively small and illiquid bond market also makes it hard for big investors to trade. The vast majority of its outstanding 316 billion-euro debt is held by official lenders, with only about 40 billion euros trading in the market.
That is a fraction of the 2 trillion euros or so in debt that trades in markets such as Germany and France.
For other investors, Greece has offered exciting returns and the upcoming auction will present them with a new opportunity, particularly given the generally bullish mood towards "risk assets," including emerging markets and high-yield debt.
Those who stuck with Greece reaped returns of more than 40 percent in U.S. dollar terms last year - the best in Europe - as two and five-year Greek bond yields fell, touching record lows recently.
Among those looking at the new debt sale is Mark Dowding, a portfolio manager at BlueBay Asset Management.
"The only Grexit we think we're going to see is a Greek exit from the bailout," he said. He was referring to speculation during Greece's financial troubles that it would be forced to leave the euro.
"We would certainly consider adding to our holdings on an attractive new issue," he added
A banker who has worked closely with the Greek debt agency on recent debt sales was confident Athens would attract more mainstream funds this time.
"A portion of real money focused, buy-and-hold investors have returned to this market now," the banker said, citing for instance strong demand at a recent covered bond sale from Greek lender Alpha Bank.
The money raised from the government debt sales will be part of a pot of up to 19 billion-euros together with other bond issues and unused bailout funds.
This is designed as a safety net as Greece eases itself out of the bailout. Greece is hoping to make a clean break with official lenders when the rescue package expires in August.
Jeffrey Franks, the director of the IMF's Europe office sounded a note of caution.
He told Reuters Greece had impressed with the speed of its reforms and recent over-performance with fiscal targets and the IMF did not see the need for more austerity measures this year.
However, he said longer-term improvements to the economy are still required.
"There shouldn't be a sense of complacency that even if the program completes this year that all will be good forever," he said.
(Additional reporting by Marc Jones; Graphics by Ritvik Carvalho; Editing by Anna Willard)