You have captured and documented the business problems outlined by the client and their requirements for a proposed solution.
The next step, assuming it looks viable, would be a business case restating the problem, the potential solution(s) with their costs and the potential benefits of delivering the chosen solution.
However, there is no basis for proceeding any further if no-one believes there is a problem to solve. In my opinion you, as Business Analyst, do not have to go any further at all- The proposal has been "thrown out" at the pre-business case stage. Any further time you spend would be a waste of time.
If you really feel, for completeness, that you must document something then file the document in the "Closed Projects" area together with the emails from the other business leaders illustrating the decision that there is no problem to fix. If there are no emails then I would hope there would be meeting minutes or something documenting the discussion and decision. If not, and it was all verbal, then personally I would go no further with it. It should not be down to you to remember, interpret and document their verbal discussions.
If you have to submit an overall findings document to senior management then I would add an appendix to the problem statement and requirements document and within that appendix summarise each interview you did: 1. Date & time of interview, 2. who was present, 3. summarised viewpoint capturing the thought that there is no business problem. This can (and probably should) be as simple as stating "[The interviewed person] could not agree that that stated business problem exists". Stick to bare facts and leave out any emotion. Then submit the overall document for review at a senior level with a recommendation that further more detailed analysis would be required to understand whether there is, or is not, an actual problem given that the relevant personnel do not believe there is a problem. I would only proceed with the more detailed analysis if authorised to do so by senior management.