The Moroccan midfielder insists the former club captain and current first-team coach has got what it takes to replace John McGlynn as the new Tynecastle manager.
The Gorgie club are understood to be considering a number of candidates including former manager and club record scorer John Robertson, one-time Jambos assistant boss Peter Houston and sacked Bristol City manager Derek McInnes.
Taouil, however, has led the calls for the interim boss to keep the job full-time.
He said: "I would like Gary to get the job because I know what Hearts means to him. I know how much of a Hearts man he is and how much he loves the club.
"It would be the perfect job for him. Not only because he is a real Hearts fan, but because he has his badges. He is capable of doing it and knows football really well. He knows Scotland really well.
"So I would say why not Gary? But then it's not me to make the that decision."