The Gelsenkirchen club sacked Huub Stevens after seeing the side fall away from the leading pack in the Bundesliga after a strong start, and having qualified for the last 16 of the Champions League.
Mainz are among the surprise packages in the German top tier this season, and Kahn believes Schalke could do a lot worse than bringing Tuchel on board at the Veltins Arena.
“Mainz clearly have a very good coach who has brought the team consistency using a systematic approach, and he has made his mark,” the former Bayern Munich shot-stopper told Bild.
“A coach like Tuchel could do very well for Schalke, I imagine.”
Kahn highlighted Bavarian attacker Franck Ribery as his star of the Bundesliga so far this season, but also hailed the signings of Javi Martinez, Dante and Borussia Dortmund starlet Marco Reus.
“The single player that stands out for me is Franck Ribery,” he continued.
“Among the top transfers are, for me, Reus, Martinez and Dante.
“Of the goalies, [Rene] Adler and [Roman] Weidenfeller have shown the most excellence.”