Reports earlier this week claimed that the Bundesliga side were looking to offer the academy graduate an opportunity to gain regular first-team football in Germany.
Arsenal are said to be open to a deal providing that Nelson extends his contract at the Emirates Stadium, and Nagelsmann has suggested that talks are progressing in a positive manner.
The 31-year-old told reporters: "We've taken an interest in Reiss Nelson, I can disclose that, but nothing is set in stone as there are still things to clear up.
"If it all works out, we'll have a player with great pace who can do a lot with the ball."
The teenager has made eight starts and eight substitute appearances for the North London outfit.