If the leak is coming from the back of the washer, the problem may be attributed to either a leaking water inlet valve, or the associated internal hoses that run from the valve to the dispenser. The following link explains how to access the inside of the washer and/or replace the valve (if required):http://www.fixya.com/support/r600647-replacing_water_inlet_valve_kenmore
If the leak is coming from under the front of the washer, the problem may be the drain pump. These pumps can develop cracks and start leaking. they are non-serviceable and will require replacing is defective. The following link explains how:
Inspect all internal hoses and hose connections as well. There are two drain hoses on the water pump, and several small hoses near the water inlet valve. These hoses can develop leaks over time.
If the leak appears to be coming from the bottom of the wash tub, you may have a leaking tub seal, or cracked wash tub (worst case scenario). You will see tell-tale signs of water marks on the gearcase (transmission) if this were the case.
On the lower right hand side of the wash tub is an air dome with a small rubber air hoses attached. Make sure this hose is still attached and has no leaks. The air hose can slip off the nipple it is attached to and water will begin to pour out of the washer when it starts to fill. This will be an "attention-getting" leak as water will gush everywhere. Double check the air hose just in case.
If parts are required, you can purchase from any of the following websites
All these sites offer great service with competitive pricing, so shop all of them for the best deals.
If you have any questions about this repair, or require additional assistance, please let me know. I hope you find this helpful.