He is expected to travel to London to seal the deal over the weekend, pending agreement on paperwork, according to The Telegraph.
The former Roma boss would replace Jose Mourinho, who was sacked after 17 months at the club in April.
Spurs seem destined for a rebuild this summer, with several players rumoured to be leaving for new pastures.
Harry Kane's departure seems more likely than ever after another season without silverware.
Although eyebrows are being raised at Fonseca's arrival, chairman Daniel Levy will be hoping he is the man for the job.
The new gaffer will look to bring in some trusted players from his time at the Stadio Olimpico.
According to La Repubblica, the three stars the Portuguese wants to bring with him are Gianluca Mancini, Lorenzo Pellegrini and Gonzalo Villar.
Transfer budget may be a big factor in this, however, and was one of the main reasons Antonio Conte's appointment at Tottenham fell through.
Mancini is a highly-rated centre-back, and Villar a 23-year-old Spain international.
Pellegrini, meanwhile, could be available for a cut-price this summer as he has a £30million release clause in his contract, which expires in 2022.
Spurs will have to battle with Barcelona, Manchester United and Liverpool, who are also keen on the Italian international.
Levy has a reputation for being hesitant to splash the cash, and it's still unknown if Fonseca's three wishes will be granted.