Spurs have been forced to look at alternative targets after ending their interest in former head coach Mauricio Pochettino.
Paris Saint-Germain have triggered a one-year extension in his contract tying him to the club until 2023 but in any case, sources have told ESPN that Pochettino has not shown any firm willingness to leave and instead has been discussing transfer targets for next season with the Ligue 1 club's hierarchy.
Pochettino remains fond of Tottenham after spending five-and-a-half years at the club prior to his sacking in November 2019 but Spurs face a hugely difficult task in prising him away from the Parc des Princes and have therefore begun speaking to Conte.
The Italian left Inter Milan after guiding them to their 19th Serie A title last season and, significantly, is therefore available without requiring Spurs to pay any compensation. Inter named ex-Lazio boss Simone Inzaghi as Conte's successor on Thursday.
Talks are said to be progressing well with chairman Daniel Levy keen to resolve the managerial situation before turning his attention to future of Kane, who has asked to leave the club.
It remains to be seen whether Conte's possible appointment is enough to convince Kane to change his mind, although Spurs are reluctant to sell in any case given his importance to the team and the fact he has three years remaining on his current £200,000-a-week contract.
Kane's future has been one key subject of discussion during negotiations with Conte. Reports in Italy also suggesting the two parties are still some way apart over Conte's wage demands.
Spurs are also exploring the possibility of bringing in former Juventus sporting director Fabio Paratici to work alongside Conte in an as yet unspecified capacity.