Yeh its possible on a B6 as they both use the same independent rear suspension, you just need to swap the subframe for a quattro one.
On a B5 the FWD models have a torsion beam, and the quattros have a subframe and independent suspension, so the shape of the rear floorpan is completely different.
I'd imagine the cheapest way you'll achieve it is to buy a scabby early quattro, they come up on ebay for not much more than 500quid for early 2.6 v6 models, less if they're broken in some way. Then swap all the nice bits/engine etc from your FWD into it, assuming of course you already have one. If you dont have any B5 at the moment, then simply buying a quattro straight out is by far the best option, not least because its simply less hassle, and will be much cheaper to insure and whatnot being as its a standard car.