The 18-year-old is a graduate of Arsenal's academy and he earned his full Premier League debut under former boss Arsene Wenger against Southampton last term.
However, the midfielder still remains down the pecking order at the Emirates and his time in north London looks to be coming to an end.
Nelson's current deal is set to expire at the end of the campaign and it's understood he isn't keen on penning an extension over fears about a lack of opportunities.
Nagelsmann has confirmed Hoffenheim are keen on signing the teenager but admits they still need to work out a few details ahead of Friday's deadline.
"We've taken an interest in Reiss Nelson, I can disclose that,' said Nagelsmann. "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."