Best advice i can give is to buy it
NOW and for as long as you can. There are 3 warranty "types"... Normal 3yr, 1 or 2 years extended for the 4th & 5th year, and then Audi used approved warranty. And even then the extra 4th and 5th year warranty is different if bought from new opposed to the warranty being bought near your 4th year. The added extended warranty has added complications like mileage and excess fees. I had an A3 and extended the warranty when the car was 3yrs old, and i extended it for an extra 2yrs, thus covering the yrs 4 and 5, the warranty WASNT transferable to a new owner. It is tied to that owner and the car together. If the warranty is bought for 5yrs at the point of buying the car new, then the warranty
IS transferable.
Also, you may want to see my following post on another forum. It shows you the amount of faf that I had to go through to get an extended warranty and the cost. Read it to the end to see the amount of ridiculousness the Audi system is.
https://www.audi-sport.net/xf/threads/audi-extended-warranty-wtf.307569/
Edit: I should have read your post more clearly! your not buying new? then you cant buy the extended warranty until the existing 3yrs is in the last month of validity. No dealer will help you as you cannot extended unless when buying new or at the last month. Are you buying from an Audi Dealer? if you are then ask them to give you the date of when the warranty is due for renewal.
Also, the dealer WILL NOT give you a better quote. It is all done online via machines. No calls to Audi support or whatever will help. This is the only way.
The way i see it, and the only real option you have, is to wait until the existing warranty is out and then buy 1 more year extended warranty. you will get the options that are best for you when you go online for a quote here:
https://insurewithaudi.co.uk/extended-warranty?r=false