Answers: The front pump inside the transmission is leak.
The transmissions in the Ford Taurus are other a problem.
Unfortunately, your transmission will hold to be removed to fix the front pump leak. This is a extremely costly, labor intensive job. You should ask yourself, if it will be worth it to fix on a 13 year ancient car. You might be better bad getting a new motor.
Good luck!
Are you positive that it is transmission grease and not motor oil? The ford motor are certain to develope a rear chief seal escape which would leak out of the nouns you describe. I would double check and make sure it's nouns oil. If it is, afterwards you may need to tighten up the bolts on the nouns pan.
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