The Italian – who has been crucial to the company’s success – has suffered health problems following a recent surgery which have led Ferrari to appoint ex-Marlboro executive Louis Camilleri in his place.
Two-time world champion Alonso left the famous Italian constructor, with whom he came second in three seasons but never won a title, for McLaren in 2015 in the hope that the Woking-based outfit would be more competitive.
But that gamble has backfired badly with Alonso enduring three-and-a-half frustrating seasons in which his best finish has been fifth. Alonso suffered another forgettable weekend at the German Grand Prix with his 20th DNF for the team.
McLaren had hoped to be closer to the front of the grid this season having swapped from Honda engines to Renault but they are seventh of 10 teams in the constructors standings having endured another turbulent campaign at the halfway mark.
It has been suggested that Alonso could soon retire from F1 to focus on his World Endurance Championship commitments and that the only way the 36-year-old would opt to stay would be to get into a seat at a championship-challenging team.
But Mercedes have tied down Lewis Hamilton and Valtteri Bottas while Daniel Ricciardo is likely to sign a new contract with Red Bull, who also have Max Verstappen committed for the long term.
That leaves only a possible Ferrari seat alongside Sebastian Vettel – with Kimi Raikkonen coming to the end of his career, this his 16th season – if Alonso wants to be back fighting at the front of the grid again.
Marchionne had previously ruled out the possibility of an Alonso return to Maranello but Sky Sports F1 analyst Brundle, himself a former McLaren driver, believes the veteran will be making calls following the team’s shake-up at the top.
“I’m very sorry to hear that Sergio Marchionne, the Ferrari boss, is very unwell and not returning,” Brundle wrote in his Sky Sports column after Hockenheim.
“This will have a big impact on the imminent direction of Ferrari and probably F1 too.
“I’m pretty sure that Fernando Alonso will be having a word with the new boss Louis Camilleri in one last desperate attempt to regain a winning car.
“Judging by his on-track performance and radio transmissions in Hockenheim he’s at the end of his tether otherwise.”
The 2018 F1 season returns with the Hungarian Grand Prix this Sunday, the final race before the month-long mid-season break.