Here's a report that is worth mentioning but should also be taken with a grain of salt. Supposedly, some devs over at XDA figured out the serial number patterns for the LG-made Google Nexus 4 phones, and through extrapolation have determined that only 375,000 of the devices have sold since their debut late last year. Of course, it's no secret that the phone keeps selling out in the Google Play Store, and is currently in that status as of now. Obviously, this is probably due to both high demand and a tight constraint on supply from Google. It could also be difficulty within LG to build enough of the phones and still keep back enough parts for their own Optimus G flagship. More than likely, all of these reasons are true to varying degrees.

Regardless, according to the analysis by XDA members after figuring out the Nexus 4 numbering scheme, it looks like less than half a million of the devices have been sold, (around 375,000 to be more precise). Here's a quote with some of the details,

Interestingly, the Nexus 4 serial code starts with three numbers and a letter, for example 212K. The first number denotes the year, 2012, the second and third are for the month, December or the 12th month, and the last K is for Korea, the country where itís manufactured.

Further diving into the system and comparing various serial numbers, users have managed to figure out not just vague approximations, but very real numbers.

In October, for instance, there were only 70,000 Nexus 4 devices produced, then 90,000 in November, and 210,000 in December. Subsequently, it was discovered that phones are quickly being made after being ordered, with one phone made for three days and taking a week to ship from Korea to the United States. Overall, with a slight allowance, the total number comes at around 375,000 Nexus 4 units produced.

This definitely does not mean actual sales, since there is stock at carrier and retailers, but it looks like a very precise approximation.
It seems like the devs that performed this analysis have done a good job figuring out the particulars; however, we can't help but wonder if something is missing out of this puzzle, which would call their figures into question. Perhaps there are different manufacturing variants that would throw off these figures. Also, how could they be assured that they have figured out the last one in the line? Of course, it's possible they are dead-on with their calculations. If they are, do you think these numbers are disappointing, or right in line with your expectations?

Source: PhoneArena