The correct option is 'am reading'.
Explanation:
The sentence 'I ... the book. You may take it' indicates that the action of reading is happening at the moment of speaking. The phrase 'You may take it' suggests that the speaker is currently engaged in reading the book and is now willing to let someone else have it.
Therefore, the correct tense to use is the present continuous (also known as present progressive), which is formed using 'am/is/are + verb-ing'. In this case, since the subject is 'I', we use 'am reading'.
The completed sentence is: 'I am reading the book. You may take it.'