The 48-year-old Portuguese would fill the vacancy on a full-time basis and replace his compatriot Jose Mourinho who was sacked in April -- Mourinho has since taken over the reins at Fonseca's old club Roma.
Ryan Mason was put in caretaker charge until the end of the season as Spurs finished a disappointing seventh in the Premier League.
Spurs have turned to Fonseca after talks with former Inter Milan coach Antonio Conte broke down.
The club have already appointed a new sporting director in Fabio Paratici, who has joined after 11 years at Juventus.
However, Spurs supremo Daniel Levy's efforts to replace Mourinho -- who was fired days away from the League Cup final clash with Manchester City -- have been less successful.
Spurs had made Leicester manager Brendan Rodgers their top target after Leipzig's Julian Nagelsmann agreed to take the Bayern Munich post.