Spurs have so far struggled to appoint a permanent replacement for Jose Mourinho -- who was sacked in April -- having explored the possibility of Mauricio Pochettino returning to the club and Antonio Conte taking charge.
Sources have told ESPN that a three-year contract has been discussed with 48-year-old Fonseca, who left Roma last month and has subsequently been replaced by Mourinho.
It remains possible that Spurs could turn to Erik ten Hag despite his decision to sign an extension to his contract at Ajax but Fonseca is now considered the front-runner for the position.
Tottenham are keen to have a new manager in place before turning their attentions to keeping Harry Kane at the club.
Kane's future was one of the subjects discussed during Conte's conversations with the club and it remains to be seen whether Fonseca's appointment would be enough for Kane to have a change of heart and want to stay.
Pochettino's return would have made a far stronger case but sources have told ESPN that Paris Saint-Germain were always confident he would stay at the club and has been discussing transfer targets for next season with the hierarchy for some time.
Conte is thought to have had differing views over the club's direction and although there were also disagreements over his wage demands, the Italian told Gazzetta dello Sport: "Money is not my obsession. I look at projects and I'm ready to stay at home if they don't convince me.
"I like difficult challenges but if there is something with a club that does not convince me, I prefer to say 'no, thank you.'"
Fonseca could join Fabio Paratici at Tottenham. The 48-year-old is expected to become Spurs' new sporting director after leaving Juventus last week.