It is very difficult to come up with a single figure for a large cathedral because, as you note, they took a very long time to make. Generally a cathedral would evolve a lot over time, often starting out much smaller and more modest then being expanded or added to over centuries

For example the current nave of Worcester Cathedral was made in the 14th century but there was a gap of almost 70 years between the construction of the north and south sides thanks to the interruption of the Black Death – it is noticeable that the quality of the workmanship on the later southern side is lower, perhaps due to more expensive labour and the lost of institutional skills.

The same cathedral has been through multiple towers (they kept collapsing), at one point the cathedral bell tower was even a separate building entirely. Nobody ever sat down with a budget then comissioned the current complex in it's current form.

I was able to find some costs for these individual constructions though, the transept of Gloucester Abbey was rebuilt between 1368 and 1373 at a cost of £781.

This was the southern transept, the exterior walls and turrets remained original but the windows and interior were rebuilt, along with it seems much of the roof, re-using the original materials in many cases. I have no idea how this compares to the cost of building the structure entire, but here is a link to the floor plan of Gloucester Cathedral, you can see that the southern transept is a small portion of the building:

http://www.ajhw.co.uk/books/book350/book350k/image51big.png

Of course how much was £781 in the late 14th century? From the same source and in the same time period, that is enough to buy somewhere around 180,000 gallons of ale, rent a cottage for over 3000 years, fully armour over forty knights or pay a master mason for over a hundred and twenty years. Given it was a five year project it likely employed several such master masons along with a large number of cheaper labourers, though they would still have likely been paid half as much.

The Costs and Values from:

http://medieval.ucdavis.edu/120D/Money.html

South Transept Archaeological Report:

http://www.bgas.org.uk/publications/gcar/gcar-99-ab.pdf

For reference, we can use the Washington cathedral mentioned by /u/tyinsf It also happens to be the sixth largest cathedral in the world, and is suitably gothic. The land cost differences can be basically ignored, since you can choose where to build, and that's a separate factor.

The cathedral cost $65M and was built between 1907 and 1990. We can use those two dates, and calculate using inflation to get a rough estimate. The oldest good records of inflation I can find go back to 1913, so we'll just use that.

$65M in 1990 is $123M today. $65M in 1913 is $1620M today.

If we take a year around the middle like 1950, you get $665M today.

Another estimate source is repair costs. Broadly speaking, most structures require a few percent of their value a year in maintenance costs. A common number is 5% of the value of the structure a year is required to maintain it. This tends to underestimate for cheap structures and overestimate for expensive ones. We can get an idea of those with a quick search online, and then multiply out to get estimates as well. I'll leave that to your discretion.

Of course, one of the problems is that the longer it takes you to build something, the more expensive it is. Building faster is more expensive in the moment, but cheaper overall. Based on all these factors, I'd probably estimate the project at around $500M if you could gather the funding to do it more quickly.

People like to give ridiculous estimates for things like this, but I find that completely absurd. Consider that the Burj Khalifa cost $1.6B, about 3x my estimate, but it's the tallest building in the world by far, is 8x taller, and has 40x the interior area. That means I'm estimating the cathedral costs over 13x as much per square foot as the Burj Khalifa. I'm estimating a cost of over $6000/ft^2. For comparison, an average American house might cost $150/ft^2, skyscrapers (including the Burj Khalifa, although it had access to cheaper labour) are usually built around $500/ft^2. For higher end comparisons, the One World Trade Center comes in at around $1100/ft^2, and the lavish paradise that is the new Apple Park is only around $1750/ft^2.

This source also estimates the cost of the Chartres cathedral, which is a banger of a cathedral, as well as it's other most expensive estimates at just shy of $600M.