It depends on the more subtle meaning you wish to convey.
The obvious solution would be to combine it into one sentence:
Rebecca lived in the same building as my wife and I, and was one our closest friends.
However, this makes Rebecca a "joint" friend of you and your wife together, not necessarily a friend of each of you, that each of you might engage with separately.
This is a problem with the English language; 'friend' is a vague word.
In most marriages (I am aware of) both men and women have close friends that are friendly with, but not close friends with, their spouse. A "close" friend is generally somebody with whom we have a mutual understanding of more extreme aspects of our emotions and personality; that has seen us in love, joy, grief or anger, dejected or hurt, frightened or worried about something (like the health of themselves or their own family members). A close friend is a kind of platonic partner on the journey of life, so you can each see these details in each other and still want to hang out with each other.
I should also note, that while developing that kind of closeness with a friend takes time, time and frequency alone do not make a close friend; it requires this more raw exposure. Just because Rebecca comes to all your parties and you leave for work at the same time every day, does not make her a close friend; any more than your mailman or coworkers are all your close friends.
Which brings us back to Rebecca. Say your wife leaves town for some reason, to help her sister deal with putting their senile father in a retirement home. You are alone for a week, staying behind for your job. If Rebecca is a close friend, and next door, she knows this. In the non-sexual friend sense, can you invite her to split a pizza at the joint you all usually frequent? Can you go to her apartment and watch a movie together? Can you ask her to some activity you both enjoy, a concert or bowling or darts in a pub, or cooking together?
Do you two have anything to talk about besides your wife?
If any of that sounds like a weird ask, to you or Rebecca, she is not really one of your closest friends, she is a friend of some distance. In which case, "One of mine too, I suppose" is an odd sentence, it sounds like a guess, and whether or not somebody is one of your closest friends should not be a guess.
But if she is, I'd suggest something more definitive:
Rebecca lived in the building and was one of my wife's closest friends. And one of my own.
(Yes, I know it is a fragment, intentionally to emphasize Rebecca is separately your wife's close friend, and your close friend independent of your relationship with your wife; i.e. if you got divorced or your wife died, you would still consider Rebecca one of your closest friends).
Clarity first, brevity second!
As written, these relationships may not be exactly what you intended. The idea of "if asked, I would say" implies you have more clarity to offer and did not. If you are going to write that in as an introduction to this greater clarity, get rid of it, and just provide the greater clarity without waiting to be asked.
A narrator might conceal some things for plot purposes or narrator-character-building, but if you aren't going to conceal it for even one sentence, just make it clear from the start, because a convoluted approach is just filler and confusing to unravel. You want your readers in suspense, perhaps not knowing what comes next, but not actually confused by what the text on the page is supposed to mean. In this case, about the personal relationship between you and Rebecca.