Apple’s MacBook Air computer will be getting an update and a big price reduction in the third quarter to compete with the next generation of ultrabooks, according to a recent report.

Citing “sources in the upstream supply chain,” DigiTimes is reporting this morning that Apple will be releaseing a $799 MacBook Air sometime in the third quarter. The new model would be aimed to compete with the newest wave of ultrabooks. Produced by companies like Asus and priced around $700, these thin, lightweight notebooks have often been characterized as the PC market’s answer to the MacBook Air.

The MacBook Air currently comes in two basic models – 11-inch and 13-inch. The cheapest model – the 11-inch with 64GB of storage – starts at $999. From there the price ranges all the way up to $1,599 for the 13-inch 256GB model. A $799 MacBook Air would represent a price cut of $200. DigiTimes’s gives no information about the technical specifications of the new MacBook Air, only the price.

Of course, this is all still just rumor at this point. Given the lack of hard evidence and DigiTimes’s less-than-stellar record for rumors of this kind, it could well be the case that we will not, in fact, see an updated MacBook Air next quarter, or that if we do, it won’t be getting the $200 price cut. In other words, stick this one in your “wait and see” file.

What do you think? Would you be interested in a MacBook Air if Apple cuts the price? Let us know in the comments.