only "Ich esse die Suppe nicht." is correct. you only use "nicht" after auxiliary verbs like "kann/will/mag...": "Ich will nicht noch mehr Suppe essen."

Richtig ist "Ich esse die Suppe nicht." oder "Ich esse diese Suppe nicht." Wenn man sagen möchte, dass man lieber etwas Anderes isst, kann man auch sagen: If you want to say that you would prefer to eat something else instead you can say: "Ich esse nicht die Suppe, ich esse die Bratwurst." "Ich esse nicht die Suppe." sagt man nicht alleine. (Das wäre englische Grammatik.) "Ich esse nicht die Suppe." is not used this way. (This would be english grammar.)

I tend to agree with the respondent mashup. The location of the negation word "nicht" in a German sentence is somehow quite a trick. Usually, for a simple sentence with simple verb conjugation, similar to your sample sentence, the word "nicht" is placed at the end of such sentence. However, for a sentence that contains a modal verb, such as "können", "wollen", "möchten" (conditional of "mögen"), the negation word "nicht" is usually placed right after the conjugation of such modal verb. For instance, "Ich kann nicht diese Aufgabe machen." (I cannot do this homework.) "Ich will nicht studieren." (I do not want to study.) "Heute Abend möchte ich nicht fernsehen." (Tonight I would not like to watch television.) For a simple sentence with compound verb conjugation, such as the use of present perfect tense to describe the past action, the negation word "nicht" is usually placed before the past participle. For instance, "Ich bin im Garten nicht gespielt." (I did not play in the garden.) "Ich bin gestern zur Schule nicht gegangen." (I did not go to school yesterday.) If however, "nicht" is put in the other locations, such as, "Ich bin nicht gestern zur Schule gegangen.", or "Ich bin gestern nicht zur Schule gegangen.", the negated matter could be interpreted as "gestern" or "zur Schule" respectively, instead of "gegangen sein". [Native speakers, please kindly rectify the above presumptions should they be incorrect.] Take care and good day. / Alles Gute und schönen Tag.