Who do you want to talk to? Whom do you want to talk to? Which one is correct sentence?
It depends on what you mean by "correct". The most formal English version would be:
To whom do you want to talk?
This is because in very formal English it is wrong to split a preposition from its object. But nobody actually talks like that in spoken English.
Although your "Whom" is technically the correct word in this case, nobody really talks like that either. "Who do you want to talk to" is by far the most commonly used variant in casual, spoken English.
According to Longman English Grammar there are three possibilities for questions of the type Who were you talking to?
1 Who were you talking to? - The normal variant where "whom" has been reduced to "who".
2 Whom were you talking to? - Also possible. Less frequent.
3 To whom were you talking to? -This is very formal. You can find this question form in written, very formal language.
When the question words are used alone it is still
4 With whom? To whom? For whom?
The correct sentence is:
Whom do you want to talk to?
The standard way to tell, is to replace who with he/she and whom with him/her, then re-arrange the sentence so it makes sense:
For instance: "whom do you want to talk to" becomes "do you want to talk to him", which sounds correct.
Whereas: "who do you want to talk to" becomes "do you want to talk to he" which is clearly incorrect.