By Tanya Agrawal(Reuters) - U.S. stocks were set for a lower open on Tuesday as investors remained cautious ahead of a two-day Federal Reserve meeting and as the Greek debt crisis showed no signs of abating.The central bank is unlikely to raise rates in this meeting but investors will watch for any hints from Fed Chair Janet Yellen at a press conference after the meeting on Wednesday about the timing of a possible rate increase.The Fed has said it remains data-dependent and will raise rates only when it sees an improvement in the economy. Second-quarter data points to a recovery after a halt in growth earlier in the year.U.S. housing starts fell in May after a hefty increase the previous month, but a surge in permits for future construction to a near eight-year high suggested the pullback was temporary and pointed to underlying strength in housing."Investors are not expecting a whole lot from the Fed meeting," said Scott Brown, chief economist at Raymond James in St. Petersburg, Florida. Brown expects a rate hike in September."The market is still anxious about Greece and would like the situation to be dealt with one way or another. The week-after-week uncertainty isn't good for the market."World markets were down with European shares hitting a near four-month low as financial markets braced for the possibility of Greece defaulting on its debt.Greek Finance Minister Yanis Varoufakis told a German newspaper that he is not planning to present new reform proposals at a Eurogroup meeting on Thursday, despite warnings from the rest of Europe that time is running out.There is an even chance of Greece defaulting on its debt payments, according to economists polled by Reuters, although the probability of it leaving the euro zone is still only one-in-three.S&P 500 e-minis were down 4.25 points, or 0.2 percent, with 165,831 contracts traded at 8:43 a.m. ET (1243 GMT). Nasdaq 100 e-minis were down 13.25 points, or 0.3 percent, with 16,442 contracts and Dow e-minis down 28 points, or 0.16 percent, with 7,245 contracts changing hands.Coty's shares jumped 15.9 percent to $30.20 in premarket trading, after the perfume maker won auctions to acquire hair-care, fragrance and cosmetics businesses from P&G for as much as $12 bln, according to sources. P&G was up 1.2 percent at $79.10.Avalanche Biotechnologies slumped 45.8 percent to $21.08, a day after the eye drug developer's experimental therapy showed that vision improvement was not significant. The result prompted brokerages to cut their ratings on the stock.American Airlines slipped 0.4 percent to $39.90 after it said it would push back delivery of 35 Airbus Group A320neo family jetliners by several years.(Reporting by Tanya Agrawal; Editing by Don Sebastian)Join the conversation about this story »