Jupp Heynckes returned for a fourth spell in charge of the Bundesliga leaders in September after Carlo Ancelotti was fired following a 3-0 defeat to Paris Saint-Germain in the Champions League.
Bayern had been a shadow of their former selves early in the campaign but they have impressed under the 72-year-old, only losing one game in all competitions.
Julian Nagelsmann was reportedly the number one candidate but Heynckes believes former Borussia Dortmund boss Tuchel is a strong candidate.
“I think that Thomas Tuchel has the quality to train a Bayern,” he told Bild. “I appreciate Thomas Tuchel, he made his way through the ranks at Mainz from the youth teams.
“That is a ladder you have to take: you learn the right approach, dealing with people.
“Borussia Dortmund then played great football under Tuchel, with good system. All the modern elements that are part of today’s football were available.”