If your client signs a listing agreement with you, as the listing agent you are contractually bound to put it on the MLS, unless your client has agreed to allow you to list it as a "pocket listing".
Jan, how do you know the property is not on the MLS? Do you have access to it? Because if you are looking on Realtor.com, know that not all MLS listings get put on the Realtor.com by default.
It may very well be on the MLS; you will have to have a Realtor double-check for you.
If it's not, as Rita said, it may be FSBO.