* S&P 500 looking to reach all-time intraday high
* Verizon/AT&T may make breakup bid for Vodafone: report
* Factory orders, durable goods data both on tap
* Futures up: Dow 36 pts, S&P 6.9 pts, Nasdaq 9.5 pts
NEW YORK, April 2 (Reuters) - U.S. stock index futures rose on Tuesday, pointing to a rebound from the previous session and tracking a rise in European equities.
* The gain implied by futures puts the S&P 500 again within striking distance of its all-time intraday high of 1,576.09, an important psychological level for investors.
* But moves may be limited for much of this this week in the absence of major catalysts before the closely watched U.S. monthly payrolls report on Friday. Last week, the benchmark index set a new all-time closing high after flirting with one for several sessions.
* Telecom shares will be on focus after the Financial Times' Alphaville blog wrote that Verizon Communications and AT&T have been working together on a breakup bid for British mobile operator Vodafone .
* Verizon and AT&T, both Dow components, were not active in premarket trading, but U.S. shares of Vodafone gained 5.3 percent to $29.84 before the bell. The stock was one of the biggest boosts among European shares, which rose 1 percent.
* Investors will also be looking to data on February factory orders, scheduled for release at 10 a.m. (1400 GMT). Orders are seen rising 2.9 percent, compared with a 2 percent drop in the previous month.
* February durable goods are also on tap at 10 a.m., with the release of the Institute for Supply Management-New York's March index of regional business activity due at 9:45 a.m.
* A weak reading on U.S. manufacturing sparked a decline in Monday's session, though other indicators have pointed to a strengthening U.S. economy and helped push both the Dow and S&P to record highs.
* On Tuesday, S&P 500 futures rose 6.9 points and were above fair value, a formula that evaluates pricing by taking into account interest rates, dividends and time to expiration on the contract. Dow Jones industrial average futures added 36 points and Nasdaq 100 futures rose 9.5 points.
* The S&P is up 9.5 percent so far this year while the Dow is up more than 11 percent.
* In company news, BGC Partners said it would sell its eSpeed platform to Nasdaq OMX Group for $750 million in cash.
* Health care stocks will also be in focus as planned cuts in U.S. government payments for private Medicare Advantage insurers did not materialize. Humana, which derives about two-thirds of its revenue from Medicare Advantage business, rose soared in after-hours trading on Monday.
* Apple Inc edged lower in premarket trading. On Monday, the stock was the biggest drag on both the S&P 500 and Nasdaq 100 after Fidelity Contrafund, a $92 billion fund that is the largest active shareholder in Apple, reported that it cut its stake in the iPhone maker by 10 percent during the first two months of 2013.