* Weakness in crude oil could again pressure energy names
* Avanir Pharma higher in premarket, Otsuka to buy
* Futures up: Dow 37 pts, S&P 3.75 pts, Nasdaq 12.25 pts
By Ryan Vlastelica
NEW YORK, Dec 2 (Reuters) - U.S. stock index futures were slightly higher on Tuesday, indicating a slight rebound from the previous session's broad decline, which was the S&P 500's weakest day in a month.
* Energy shares will be in focus as crude oil continues its recent volatility. U.S. crude futures were down 1.2 percent to $68.16 per barrel. While the commodity jumped on Monday, that followed a plummet of more than 10 percent last week, a decline that took it to multi-year lows.
* Declines in energy shares have corresponded with the weakness in oil, which is down more than 30 percent from a recent high. The S&P 500 energy index is the weakest industry group by far this year, and the only one to be negative for 2014.
* Apple Inc edged slightly higher in premarket trading. The tech giant lost 3.2 percent on Monday, dropping in its biggest one-day drop since September. The stock, the biggest U.S. company by market cap, was also hit by unusual trading activity shortly after the market opened, tumbling in the span of a minute in what some traders deemed a "mini-flash crash."
* Avanir Pharmaceuticals Inc rose 12.5 percent to $16.88 in premarket trading after Otsuka Pharmaceutical Co Ltd agreed to buy the company for about $3.5 billion to expand its neurologic drug portfolio.
* Investors are looking ahead to a read on October construction spending, due at 10 a.m. (1500 GMT) and seen rising by 0.6 percent. Markets may be vulnerable to a weak read, which would follow tepid reports on manufacturing on Monday and could prompt traders to take profits.
* Despite Monday's decline, equities have been strong of late and continue to hover near record levels. Major indexes closed out a sixth straight week of gains last week.
Futures snapshot at 6:57:
* S&P 500 e-minis were up 3.75 points, or 0.18 percent, with 119,123 contracts changing hands.
* Nasdaq 100 e-minis were up 12.25 points, or 0.29 percent, in volume of 17,492 contracts.
* Dow e-minis were up 37 points, or 0.21 percent, with 25,044 contracts changing hands. (Editing by Chizu Nomiyama)