The Englishman played a key role in Ferrari's most successful period in the sport. Alongside Michael Schumacher, Jean Todt and Rory Byrne, Brawn helped the Scuderia to win five drivers' World Championships and six constructors crowns between joining in 1996 and departing a decade later.
He subsequently switched to Honda and, when the Japanese marque withdrew from F1, led a management buyout that resulted in Brawn GP competing in 2009. The team won both World Championships before selling out to Mercedes.
Brawn left the Brackley-based squad at the conclusion of last season and has since stated that he is 'retired', but that has not silenced rumours that he could return if the right job comes up.
And Ferrari chief Mattiacci has added fuel to the fire by stating that his team would be keen to bring the Englishman back into Formula 1.
"Everybody would like to have Ross or would like to see Ross back at Ferrari," said Mattiacci. "He's one of the most respected personalities in F1 with the highest knowledge and pedigree.
"Everybody would be happy with somebody like Ross."
However the Italian added that bringing in Brawn would mean pairing him with current technical chief James Allison, not removing the incumbent.
"James is the technical director and I want to start from that point. To tango you have to have two.
"Maybe Ross is happy with what he is doing," he concluded.
In total, Brawn has been part of 16 World Championship wins, including all seven of Michael Schumacher's drivers' titles.