The former Chelsea boss has emerged as a leading candidate to replace Jose Mourinho, and Spurs also want to bring in former Juventus sporting director Fabio Paratici who has previously worked with Conte.
If Paratici - who is also a free agent - is brought in by Tottenham, it is unclear where that would leave current technical performance director Steve Hitchen.
Conte left Inter Milan last month having guided them to their first Serie A title in 11 years. Tottenham made contact with the Italian, who won the Premier League and FA Cup with Chelsea during two years in charge at Stamford Bridge, last Thursday.
Spurs continue to explore bringing Mauricio Pochettino back to the club, but opened talks with Conte last week as they search for Mourinho’s replacement.
Ryan Mason in April took interim charge for the remainder of the season as Tottenham lost the Carabao Cup Final and finished a disappointing seventh place in the Premier League.
Chairman Daniel Levy has pledged to appoint an “attacking and entertaining” manager and has also made an attempt to re-appoint Mauricio Pochettino.
But Paris Saint-Germain are reluctant to let the Argentine leave to return to north London.