Girls, would it be weird to ask a female co-worker if she has any single friends or acquaintances who might be interested in me?

I've been single for awhile and not having much success finding anybody. I have a couple of female co-workers who are very sweet and I'm comfortable talking to them. They are already taken, but I'd really like to know if they might know anyone who might be available and who they could connect me with. Just not sure if it would be weird/desperate of me to bring this up to them.

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UPDATE: I finally worked up the courage last week to ask one of my co-workers about this. She was super sweet about it and said she'd find out if any of her friends would be interested. She said she'd let me know once she figures it out. I don't work with her everyday but hopefully next time I do she'll have an answer for me. She also promised she wouldn't tell anybody else at work about it, which I appreciate :)
Girls, would it be weird to ask a female co-worker if she has any single friends or acquaintances who might be interested in me?
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