Jonas wants the Giver to keep memories of music for himself.
The Giver shares many memories with Jonas, because it is his job as Giver of Memory. Jonas’s job as Receiver of Memory is to learn as much as he can. The Giver tries to give Jonas good memories to balance the bad ones, so that he is not overwhelmed with pain.
"Music," The Giver said, smiling. "I began to hear something truly remarkable, and it is called music. I'll give you some before I go." (ch 21)
Jonas tells Giver that he wants him to keep the music “to have with you, when I'm gone." This is because Jonas is planning to flee the community, since he has learned that release means murder. He has recently seen his father kill a newborn baby, and this helped him to understand that Sameness was not a good thing for his community, because it turned the people in monsters without them even realizing it.
The fact that Jonas is so considerate demonstrates an important part of his character. He is sensitive, which makes him a good Receiver but also helps him build a relationship with his new mentor, the Giver.
Lowry, Lois (1993-04-26). The Giver (Newbery Medal Book). Houghton Mifflin Harcourt. Kindle Edition.