current Max range = 6100 miles
Earth circumference = 24901 miles
you would need fuel in fuselage for 18801 extra miles or about 3 times current Max range
and therefore 3 times current main tank capacity in the fuselage
(not considering increased GW effects on range which is stupid but ok to make this silly point)
fuel for current max range = 48445gals
6.7 lbs/gal * 48445 gals = 324581 lbs (you probably see what's coming)
weight of fuel needed in fuselage = (324581*3)lbs = 973774 lbs
This is an order of MAGNITUDE greater in weight than the current max passenger weight. The whole plane weighs less than 800,000!!!!
Thank you for playing.
There are several problems with your numbers which make the amount of additional fuel required much less than an order of magnitude.
The biggest problem is in your choice of the circumference of the earth as the required distance. None of the "around the world" flights have taken place over the equator. In fact most of them have taken place mostly north of 30 degrees. So the actual flight distance will be substantially less than ~24000 mi, probably more like 16 to 18000 miles.
Second, the range you state for a 747 includes a significant amount of fuel reserves per FAA mandates to allow for diversions and wind conditions. Since any "around the world" attempt would be flown from west to east and using the jet stream as much as possible and since this would be an experimental flight, not a passenger flight, no fuel reserves would be required.
Yes, GW would affect the range, but at the end of flight you'll be much lighter than a regular, empty 747, so you'll regain some of that loss. Also, you'd be flying at the maximum altitude that you can reach for the entire flight and at the minimum airspeed (this is another thing that the standard range numbers do not include since it would never be done on a passenger flight due to safety concerns).
Add to that the fact that you would run the engines as lean possible since you wouldn't care about reducing their lifespan (yet another thing not included in the standard range number).
Also, anyone who was serious about attempting this, would go over the airframe and clean it up as much as possible, so it would have significantly less parasitic drag than the average 747.
Add all this up and I think the numbers would be closer to 3 times more gas rather than 10 times. Still a hell of a lot of extra gas and it might not be possible. But I think its a heck of lot closer than you think.