Anyone can suggest a shiduch. Really.
You know 2 people and you think that they might be compatible. Then you can go ahead and suggest it.
But too often people just don't. Why is that?
After an unscientific survey, it seems that too many people are afraid that they might get a response like "How could you even suggest that to me?" But when I asked the follow up question, "If you ever made a suggestion, did you get such a response?" almost always the answer is "At worst, they politely thanked me and moved on."
So then, what is the big deal to make a suggestion. You won't have to be the official shadchen and do all that work. You're just making a suggestion. And they can take it wherever they want; they can decide to meet or not.
If you are still uncomfortable with the idea of making a suggestion, you might present it using words like, "Can I share a shiduch idea with you for your son/ daughter/ sister/ brother/ yourself?" And once you get the permission, you can continue. You say the context in which you know him and what he seems like to you. And why you thought he might be a possible match for her. That's all. Short and to the point.
"I worked together with Yossi S. on a few projects. What I see of him is that he has drive and is dedicated to making things happen. He is good with the team, he knows how to calm people down when the going gets tough. He has a good sense of balance of working hard and knowing when to kick back. I thought he might be a good match for your Chanie because they both are passionate about being involved in the community, both share a sense of adventure and fun. She is probably a little more laid back than him, but they would balance each other. I don't know anything about his background, since I only know him from work and we don't really get into those types of conversations. "
In this way, you don't have to be concerned that they might be insulted by your suggestion - you simply are sharing about him based on the context in which you know him. If they find something that doesn't seem compatible that is beyond your context... well you didn't know.
And trust yourself. You think it is a real possibility... if you don't say it, it just might not be suggested.
You just may be the shliach for that shiduch. Take a deep breath and make that phone call.
It' a shiduch waiting to happen.