Werner's contract at the Red Bull Arena is set to expire at the end of this season and the Bundesliga champions have been heavily linked with a swoop for the 23-year-old.
Leipzig CEO Oliver Mintzlaff admitted in April that Werner was unlikely to sign a new deal, meaning the club may be forced to sell him now or risk of losing the striker on a free transfer next summer.
Werner was among the scorers as Leipzig opened their Bundesliga campaign with a 4-0 victory at newly promoted Union Berlin on Sunday.
Speaking after that game, Nagelsmann reiterated his desire to keep the Germany international at the club.
"Of course we want to keep him, he is an important, good player and in my head he is my player,” he said. “He will know for himself what is most important for his career.”
Leipzig sporting director Markus Krosche hinted that Werner’s future could be decided one way or another before the transfer deadline at the end of this month.
"There's nothing to say about this. He's with us - we've been saying the same thing for weeks because that is the case,” he said. “There's definitely going to be a decision in the coming days, Timo Werner and his advisor want that too.
"That's Timo's decision, we did everything as a club and we gave him all the appreciation we can give as a club.
"He's a player in this squad, and we've seen today [vs Union Berlin] how much he can help us achieve our goals.”
Werner has developed into one of Bundesliga’s most feared strikers since joining Leipzig from Stuttgart in the summer of 2016.
He has hit 62 goals in 116 appearances for the club, including 19 across all competitions last season, helping Leipzig secure a top-three spot in the Bundesliga and reach the DFB-Pokal final.
The 23-year-old has also scored 10 goals in 25 appearances for Germany and was part of Joachim Low's World Cup squad last year in Russia.