The 23-year-old Werner has enjoyed another fine season for the Bundesliga outfit, scoring 16 times and adding seven assists in 30 appearances for Leipzig.
His performances have helped the club to third place in the league this year and a guaranteed return to the Champions League next term.
Reports have surfaced suggesting Werner wants to leave Leipzig this summer with Bayern Munich his destination, and the fact he has not decided to extend his deal has only fueled such talk.
However, Mintzlaff has insisted nothing had been decided yet, denying any conversations about a move to the Bundesliga champions have occurred.
"We haven't spoken to Timo Werner about Bayern Munich, but what the player wanted to do was important for us as he wanted to see how the season would go,” Mintzlaff told Sky Sports. “Last year we certainly didn't play football like we did in the season before.
“We have submitted an offer and we know that Timo would rather not extend – but that can still change.”
Mintzlaff believes Werner has grown with Leipzig and can understand why he might want to move on in the future.
However, he is also hopeful the return to the Champions League, combined with the arrival of highly regarded Hoffenheim coach Julian Nagelsmann will also tempt Werner to stay.
“He has matured with us as a personality and he's willing to take the next step now. We have always said that we do not want to stand in the way of a player's career if he has decided to leave us.
"As long as we qualify for the Champions League, we believe that - with the new coach Julian Nagelsmann - it would certainly also be a platform where Timo Werner can develop and feel good."
However, even if Werner does wish to leave, Mintzlaff denied that Bayern Munich is his only possible destination.
Other clubs, such as Liverpool, have been linked to Werner in the past and the Leipzig CEO believes the Reds, as well as other clubs, are still in the mix to land the star man.
“Maybe he doesn't even want to go to Munich,” Mintzlaff added. “Maybe he wants to go to [Thomas] Tuchel in Paris or, I have no idea, maybe to Jurgen Klopp [at Liverpool] or Lucien Favre [at Dortmund]."