The Portuguese is leaving the Serie A outfit at the end of the season, with Jose Mourinho taking over from him.
The Special One was sacked by Spurs a fortnight ago, and the North Londoners have been linked with a couple of names already.
Fonseca is the latest, and he fits the bill given that chairman Daniel Levy wants a young manager who cherishes attacking football.
Celtic are also looking for something similar in their next manager, and it is why Eddie Howe has been tipped as favourite to succeed Neil Lennon.
With the former Bournemouth yet to sign with the Hoops, though, Fonseca could emerge as an option.
However, Celtic do not have the finances to pull off such a deal and it will be interesting to see how things go.
Leeds United were linked with the former Shakhtar Donetsk boss over the weekend, with Sportitalia TV journalist Gianluigi Longari claiming they recently made contact with him.
With Marcelo Bielsa yet to pen a new deal at Elland Road, it appears that the Whites are putting contingency plans in place.
It seems Celtic and Spurs could now join them in the race for the 48-year-old, with Crystal Palace, OGC Nice and Napoli also keeping tabs on him.
The Portuguese won three Ukrainian Premier League titles, three Ukrainian Cups and a Ukrainian Super Cup with Shakhtar.
Fonseca also won the Portuguese Super Cup with Porto and the Portuguese Cup with Braga, and he could be keen to prove himself in the Premier League.
In other news, Arsenal reportedly join Spurs in the race for Italian manager.