Has the drain hose been connected to your sink ? It may be joined to the sink plumbing with a pipe as shown in the image. This connection may become blocked with food deposits and fat. You can easily check and clean the pipe work. This kind of blockage will not prevent your sink from draining away but may be stuck inside the washing machine pipe.

Place a bowl underneath the sink to catch any water then disconnect the grey drain hose. Look into the end of the sink connection and remove any blockages or obstructions. If your kitchen is brand new check the end is not plugged off . Pop the waste pipe back on and select a drain cycle - the water should now flow out through the sink drain.