Discharging the rinse water into a standpipe keeps the tub clean.
Drain utility sink into washer standpipe.
You may need a special drain hose depending on the distance of the washer to the sink.
I will be putting the utility sink in the empty space between the dryer and the white wall in the picture the washing machine is immediately to the right of the dryer.
A standpipe is a vertical piece of pipe with an elbow on the bottom.
Buy a t shaped pvc joint cut the standpipe insert the t so that the cross is vertical.
The original copper pipe was 1 1 4 and the new pvc is 1 1 2.
The elbow remains filled with water preventing sewer gas from backing up into your laundry area.
Older laundry tubs drain the washing machine leaving dirt and soap scum stains.
You can install a bracket or wire ties on the back of the sink so the washer drain hose is permanently attached to the sink.
This is the new pvc drain pipe.
If you can install your washing machine in the garage and next to a utility sink then yes you can let it drain into the sink.