The correct answer is “to see”.
The verb “see” is used in the present tense in this sentence. The sentence is about the speaker’s hope to see the listener in the future. The present tense is used to talk about things that are happening now or that will happen in the future.
The verb “seen” is the past participle of the verb “see”. It is used in the past tense and the perfect tenses. In this sentence, the past participle “seen” would not make sense because the speaker is not talking about something that has already happened.
The verb “saw” is the simple past tense of the verb “see”. It is used to talk about things that happened in the past. In this sentence, the simple past tense “saw” would not make sense because the speaker is not talking about something that happened in the past.
The verb “to see” is the infinitive form of the verb “see”. It is used to talk about things that are possible or that are desired. In this sentence, the infinitive “to see” makes sense because the speaker is expressing a hope to see the listener in the future.