Heidel confirmed that Tuchel has had contacts with Schalke and Bayer Leverkusen.
Tuchel first told Mainz in January that he wanted to quit at the end of the season and repeated his wish four weeks ago, Heidel said.
Heidel said Mainz was beginning to look for another coach but declined to give any names. With limited financial means but clever management, Mainz has become a Bundesliga success story.
Tuchel has not given any reason for leaving the club. He is the second coach to leave at the end of the season. Huub Stevens, who saved Stuttgart from relegation, said on Saturday that he would not return.