The 40-year-old coach has led Mainz throughout their four-and-a-half-year stay in the Bundesliga.
He led the club to a fifth-place finish in 2011 and they are pushing for UEFA Europa League qualification this term.
Mainz are keen to keep hold of Tuchel, with the hope he can continue to take them forward.
"We are very pleased with Thomas," Heidel told Bild. "And if he wants to renew with us then it will only take a few minutes.
"In the coming weeks we will start to talk about it."
Mainz are currently seventh in the Bundesliga table, one point behind Borussia Monchengladbach, who occupy the final European spot.
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