Technically speaking sump pumps may only be used to discharge storm drainage and may not be connected to the DWV (Drain, Waste & Vent) system.
The discharge from a laundry sink is tecnically defined as sanitary waste and requires an approved Sewage Ejector Pump. Sanitary sewage may not be discharged through a sump pump.
After discussing this idea with a couple colleage's who are Plumbing inspectors we are all of the concensus opinion that you could take advantage of a rather gray area of the code providing it is not rejected by your local inspector.
If you were to cut a hole in the concrete and install a permanent sump or catch basin that would be considered a permanent fixture and as such you would be required to install an approved sewage ejector complete with a water tight lid and a vent through the roof, howver, if you use a crock or vessel sitting on the floor and fitted with a utility pump you could then make the argument that it is not a plumbing fixture but rather it is an appliance in the same manner as the washing machine or a condensate lift pump on an HVAC system (providing you do not connect a watercloset to the crock.)
As an appliance the discharge must then be connected to the house DWV system by means of an indirect waste receptor which in this case would be the washing machine standpipe.
To make an approved standpipe you would first come off the existing drain line with a 2" P-trap, then install an 18" PVC riser on the input of the P-trap. (The code minimum for a washer standpipe is 18" vertical above the trap.)
There are a number of small submersible utility pumps such as those made by "Little Giant or Wayne Pumps" that have a 3/4" garden hose connection on the output that would suffice for your needs. You could then attach an appropriate length of 3/4" garden hose and on the output end make a U shaped section of copper or aluminum tubing which could be inserted into the garden hose and connected with a radiator clamp. The Inverted U shape would then hang on the top of the standpipe to make the final connection. (The pumps are typically about $75)
For a control system you can get a submersible float switch that is made for sump pumps that has a long cord attached. The switch assembly is secured to the pump by means of a large radiator clamp and the cord goes up to your outlet. The switch cord is plugged into the outlet and the pump is then plugged into an outlet on the switch cord. Once this is set up as the water rises in the holding vessel the switch floats upward and turns the pump on. As the water level drops the switch then floats down to the horizontal position and turns the pump off. (Accessory float switches are typically about $20).
Both the washing machine and the pump can share a common standpipe.