Former Ferrari president Luca di Montezemolo admits he is "worried" about his former team.
Specialist German reports claim Sauber-Alfa Romeo team boss Frederic Vasseur has now turned down Ferrari's invitation for him to replace axed team boss Mattia Binotto.
McLaren's Andreas Seidl and Red Bull's Christian Horner also reportedly said no, with many insiders believing the role is akin to a poisoned chalice at the Maranello-based marque.
Corriere dello Sport claims that Ferrari chairman John Elkann is currently working on a three-person management solution similar to the way Red Bull handled the death of Dietrich Mateschitz.
The three-person solution would involve an overall management head, a team principal and a technical director.
Ferrari CEO Benedetto Vigna may currently be the interim boss, and he was asked this week at Milan Polytechnic university about who will ultimately replace Binotto.
"2,500 years ago, Heraclitus said 'Everything flows'," Vigna jokingly answered.
Di Montezemolo, who so successfully led Ferrari until he was ousted in 2014, commented: "I'm sorry about the situation at Ferrari and I'm worried.
"In these moments, since I really care about Ferrari, I prefer not to comment other than to note that it seems to me to be a company without a leader."