According to Heidel, Tuchel made the club aware of his intentions a few weeks ago.
But Mainz do not want to lose the popular coach, who led the club to the UEFA Europa League for the second time since joining in August 2009 thanks to Sunday's 3-2 win over Hamburg.
Heidel thanked Tuchel for his achievements this season but despite telling the club's website that they have not accepted the resignation, it appears that Tuchel's time at Mainz is at an end, with Schalke thought to be monitoring his situation closely.
Heidel said: "The discussion, which is now public, were internal for several weeks and months.
"Thomas Tuchel has a contract with us until June 30, 2015. Some time ago, he asked to terminate this agreement.
"We have not complied with this request. Then, he said, he would like to coach no club in the season 2014-15.
"You can call the resignation. The fact is, we do not want to dissolve the contract. We have not talked about this, because we wanted to not endanger the success."
