Fill in the blanks with an appropriate verb form:

They…………………….. us for a long time.

have known

The correct verb form to fill in the blank is have known. The present perfect tense of the verb "know" is have known. The context of the sentence indicates that the speaker is talking about something that has been happening for a long time, so the present perfect tense is the most appropriate tense to use.

The other options are incorrect.

• Are knowing is the present continuous tense of the verb "know".
• Knew is the simple past tense of the verb "know".
• Known is the past participle of the verb "know".