Hello,
It could be the pump among other things. Your going to have to take the cabinet off the washer to trace where the leak is coming from. Not sure of your model number but most Kenmore washers are made by Whirlpool and are removed this way: Start by removing the plastic endcaps (if you have them) at the ends of the console. This will reveal the screws to remove. Once the console screws are removed flip the console back and let it rest. Use a straight screwdriver to remove the two metal clips and then unplug the lid switch harness that was under the console. Now stand in front of the washer and rock the cabinet forward. The whole cabinet removes for access. Hope this helps.
JP, June 2006