Cockatiels are on my very short list of favorites
Tell us more about her pair. Why do they need a new home? Would you be able to interact with them before making your decision? Would she make vet records available for your vet's review prior to a decision? Do you care if they are perhaps older, maybe with chronic health problems? I know you said earlier that you can't bear the thought of losing another, so my guess is you'd prefer young, healthy birds.
Are the pair bonded, clutchmates, tame, flighted? Have they produced chicks? If one is female and older than 12-15 months, how often does she lay eggs?
Cockatiels are extraordinarily friendly, lovable birds and, partly due to that, I think most are happiest with a cagemate. I didn't mention a cockatiel to you yesterday because I don't like the thought of a single one at home alone all day. Just my bias. This pair might be a great find for you if they are tame and healthy enough to not endanger your lovie. But there are many things to consider, and the reasons some people give for wanting to rehome a bird are not always fully honest. Please be very careful for the sakes of both your aging baby and your own tender heart, but my fingers are crossed that this works out beautifully.