Oil/Grease under washer machine

Nash, your unit appears to be made by Whirlpool. (Kenmore doesn't manufacture anything, they purchase from major manufacturers and put the "kenmore" name on them) If, as I suspect, it is made by Whirlpool... the top transmission seal is failed allowing small amounts of water to enter the tranny. The water, being heavier than oil, will displace the oil through the top of the tranny... out through a "weep" hole. The weep hole is not designed to allow fluid to escape, it's designed to allow air to enter and exit the transmission housing, compensating for the heat expansion and contraction of the lubricant that should be contained within. Regardless of the manufacturer, you have a main drive system failure on your hands. It'll only get worse from here. Most manufacturers put a 5 year warranty on their drive-trains, you should call them immediately. If it's over 5 years old, it's a very expensive repair.

Normally there is no oil pan under a Washing machine unless some newer model do that I do not know. What is your make /model? This could be from melted motor grease due to out too warm weather. Is the washing M/C in a non-ac room like a garage?