The long-anticipated departure of Steve Bruce was confirmed on Wednesday, and the Magpies have now turned their attention to the highly-regarded Portuguese coach.
Fonseca was close to being appointed Tottenham Hotspur's new head coach in the summer before Nuno Espirito Santo took up the role, and could now be in place to land his first job in England.
He held an extensive Zoom meeting with the Newcastle hierarchy, and new director Amanda Staveley is supposedly a big fan of the 48-year-old.
Fonseca spent two years in charge of Roma and took charge of 101 games with the Serie A club. He did not win any silverware at the Stadio Olimpico, but won a glut of trophies with previous club Shakhtar Donetsk.
His CV boasts three consecutive Ukrainian league and cup doubles, as well as one Ukrainian Super Cup. The manager also experienced success in his native Portugal, after winning the Portuguese Cup with Braga and the Portuguese Super Cup at FC Porto.
Aside from Fonseca, a host of other names have been linked with the job and include current Rangers boss Steven Gerrard, Eddie Howe and Lucien Favre.
Antonio Conte was also widely linked with the job, but the Italian is apparently waiting for a call from Manchester United should Ole Gunnar Solskjaer be relieved of his duties at Old Trafford.
Graeme Jones is currently in interim charge, with Newcastle now turning their attention to a match against Crystal Palace on Saturday. They end October back at St James' Park when title-chasing Chelsea visit Tyneside.
The Magpies are still waiting for their first league win of the season after amassing only three points from eight games so far, leaving them 19th in the table. They were most recently beaten 3-2 by Tottenham on Sunday, in what was Bruce's final match in charge.