Each difficulty setting has its own maximum number of sockets that socketed items can
spawn with: 3 (Normal); 4 (Nightmare); 6 (Hell).
The table
here specifies the odds of
adding ... sockets to a normal quality item without sockets, using the proper
Horadric Cube recipe.
Max sockets at Item Level... for swords:
https://www.theamazonbasin.com/wiki/index.php?title=Sword (for this case consult the first table below ''One-handed'').
Adding sockets to a low (Cracked, Crude, Damaged, or Low Quality) or high quality (Superior) item requires the use of Larzuk's quest reward - as you might know.
Anya's quest reward
rare item gains Item Level = character level, thus potentially offering you some control of affix availability.
Normal:
basic claw - Nightmare:
exceptional claw - Hell:
elite claw. You could perhaps try experimenting with the affix calculator.
Point of the matter is that receiving your reward from Anya at a lowish level might in fact hurt your chances.
Good bot.