* Euro zone summit on Greece proposal to start at 1600 GMT
* U.S. May trade deficit widens less than expected
* AMD slumps after cutting quarterly revenue forecast
* Shake Shack falls after Morgan Stanley rating cut
* Futures up: Dow 27 pts, S&P 4.25 pts, Nasdaq 3.5 pts (Adds details, comment, update prices)
By Tanya Agrawal
July 7 (Reuters) - Wall Street was set to open slightly higher on Tuesday ahead of a euro zone leaders summit at which Greece will bring a proposal in a last-ditch bid to secure an aid package to keep the country in the currency club.
Greek lenders are down to their last few days of cash and the European Central Bank has tightened the noose on funding, putting pressure on Greek Prime Minister Alexis Tsipras to persuade the bloc's other 18 leaders to open negotiations fast. The summit begins at 1600 GMT in Brussels.
It is unclear how much Tsipras' new proposal would differ from others rejected in the past. Failure to reach a deal would increase the likelihood of Greece leaving the single currency.
Adding to the pressure, Finnish finance minister Stubb said the euro zone was not looking at bridge finance for Greece "at this stage". The next debt deadline for Greece is July 20 when it has to repay $3.9 billion of bonds to the ECB.
"U.S. markets really are taking their cues from what's happening outside the country as we head into the earnings season," said Paul Nolte, portfolio manager at Kingsview Asset Management in Chicago.
"Valuations are still high and earnings are going to be rough with companies adding not more than 1-3 percent year over year. We expect the market to continue moving sideways for the remainder of the year."
S&P 500 e-minis were up 4.25 points, or 0.21 percent, with 227,297 contracts traded at 8:44 a.m. ET. Nasdaq 100 e-minis were up 3.5 points, or 0.08 percent, on volume of 33,978 contracts. The Dow e-minis were up 27 points, or 0.15 percent, with 28,424 contracts changing hands.
European stock markets steadied ahead of the summit, but Asian shares fell after further losses in China despite the emergency measures.
Data showed that the U.S. trade deficit widened less than expected in May, suggesting economists might raise slightly their forecasts for economic growth in the second quarter.
A stronger dollar has slowed foreign demand for U.S. goods, while imports have gone up. The dollar index was up 0.85 percent at $97.10, its highest level in a month.
Advanced Micro Devices shares slumped 17 percent to $2.05 premarket after the chipmaker cut its quarterly revenue forecast citing weaker-than-expected PC demand.
Pinnacle Entertainment rose 9.3 percent to $40.95 after Gaming and Leisure Properties raised its offer for its real estate assets to about $5 billion, including debt.
Shake Shack fell 5.8 percent to $55.55 after Morgan Stanley cut its rating on the hamburger chain operator's stock to "underweight", according to theflyonthewall.com. (Editing by Savio D'Souza)