Ask if people want to be connected…
If you are apprehensive about connecting two people, then ask one of them if they want to be connected. Provide examples like “I believe that the other person would like to meet someone with your expertise, service or products and that you would be an asset to them. Would you like for me to introduce you sometime?”
A simple unobtrusive way is with a simple email that includes both parties contact information, and why you are doing this. Provide a reason like “I know that Joe is looking for someone in the _______ industry to learn about how he can better _______, he may be looking for your services.”
Even if the introduction does not workout immediately, it shows that you care enough to know both parties, that you remember them, they are top of mind, you are aware of their business.