People are more likely to agree to mediate if they believe that talking to the other person is either preferable to, or more likely to work than any alternatives they have thought of.
Mediation may be an unfamiliar idea and it is sometimes wrongly assumed that it will be like court or that the other person is incapable of negotiating. A chat with a mediator can help.
An initial invitation to discuss mediation from a mediator can be more effective than an approach from a lawyer or the person they are in dispute with.