I closely follow another EFL team, where there were suggestions over a couple of seasons that because the manager was signed to a particular agency, he was being encouraged to only sign new players on permanent and loan contracts from the same agency.
The facts spoke for themselves - repeated new players all represented by the same agency being signed, and mostly not up to the standard and the team suffered as a result.
The inference by others (not me) was that the manager was getting some sort of financial kick-back or bonus for every player he signed who was represented by that agency.
I suppose the question is why would any manager need an agent? Presumably their agent plays a part in discussing new or extended contracts or touting their name around if they fancy moving clubs, in the same way players need an agent. But I do think there needs to be some transparency where any manager might receive an incentive if they sign players from specific named agencies. In any case where a manager has an agent, at the very least the club chairman and secretary should know about the link.