They are moderately happy with our solution. How should the customers approach the potential suitor?
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