Tuchel has been in charge of the German club since Jurgen Klopp left in 2015.
However, relations between Tuchel, 43, and Watzke have been strained since the Dortmund team bus was damaged by an explosion on 11 April.
"We will sit down after the season and discuss how things will continue," said Watzke.
Dortmund play their final match of the Bundesliga season on Saturday when they entertain Werder Bremen (14:30 BST).
Victory will secure third-placed Dortmund a place in the Champions League group stage unless fourth-placed Hoffenheim, who have the same number of points as Dortmund, win heavily against Augsburg.
Former Borussia Monchengladbach boss Lucien Favre, 59, has been linked with Dortmund after steering Nice to a third-placed finish in Ligue 1.
Tuchel, who has one year to run on his contract, claims neither he nor his players were consulted about whether they should play the Champions League quarter-final home tie against Monaco less than 24 hours after three explosions in the area of the team bus.
Watzke denied that was the case and said the claim had annoyed him.
Borussia Dortmund boss Thomas Tuchel will have talks about his future at the end of the season, says chief executive Hans-Joachim Watzke.