The 17-year-old has broken into the first team at the Mercedes-Benz Arena this season, scoring four goals in 18 appearances.
Werner's growing reputation has seen him touted for a call-up for Germany's FIFA World Cup squad, and Stuttgart are keen to tie the promising teenager to a new deal.
"We've had some good talks and we're already at quite an advanced stage," Stuttgart's director of sport Fredi Bobic told Stuttgart Nachrichten.
"Both sides have given some very clear signals.
"There will not be any release clause (in his new contract) - we don't want to have any negative situations, but rather we want to give Timo a constant basis and a continued solid education."
The likes of Mario Gomez and Sami Khedira have progressed through Stuttgart's youth ranks before moving on to bigger clubs, but Werner has no immediate desire to seek a move elsewhere.
"I cannot envisage playing anywhere else, ever," Werner said.
"I've been at the club since 2002 and hope to stay for many more years to come."
