The Parkhead side have twice taken the 16-year-old on trial and the Congolese-born player, who has represented Sweden Under-17s, is keen to make the move.
Leif Lindstrand, the Gelfe chairman, said: "The only thing we can do is wait for the bid from Celtic. When it comes, we will decide how we should proceed. We will do what is best for Tshutshu."
Meanwhile, Kaposvari Rakocz have told their 17-year-old striker Mark Murai, who is due to go on trial at Parkhead this month, they won't stand in his way of a move to Celtic.
John Elijah, the Hungarian side's chairman, said: "When there is interest from a club like Celtic, we promise we will be very fair to Mark."