They are moderately happy with our solution. How should the customers approach the potential suitor?
What an interesting concept (and I'm being polite with the word "interesting').
Your customers, who pay for your service, should do the leg work to be your cheerleaders for your business so that you can lock in your Biggest customer (the end business buyer)?
There is absolutely no reason your customers should be talking to the "potential suitor" in a cold call (they make the outreach) scenario.
If it's a "suitor" (they are pursuing you), then they already have interest.
Your focus instead should be on how to turn "interest" (which is about as a common as bad ideas) into "motivated interest". The subtle difference being that they have a specific, motivating reason to pursue the deal with some margin of urgency and seriousness.
Normally it's the other way around. You should give your potential buyer the contact information of a few of your customers, and you have to encourage them to contact them.
That way they'll care more about what the customers have to say about your product/service. Also, something I did is to encourage users to tweet about the service, and I just gathered all that information for the potential buyer. I hope this helps!
With all due respect, that isn't a good idea. If you do feel that you'd be better off bought by this competitor it's completely OK, but having customers be matchmakers is a big no-no.
The message to both parties would be harmful to you. Customers would see this as a sign of potential abandonment of your product and therefore avoid buying it for fear of discontinued support. The acquirer-to-be would see this as an odd and unprofessional approach, either negatively affecting their potential desire to buy, or simply the valuation based on this showing of limited business acumen.
You can reach out yourself or use an advisor (independent or investment bank, depending on deal size)
Good luck, happy to help if needed