The Premier League club approached Conte for talks as they seek to fill their vacant managerial role, but the Italian is claimed to have gone cold on taking over in north London.
Tottenham are not expected to appoint Conte as things stand, but the club did not reach the point of offering the job to the former Chelsea boss.
It is claimed that during talks Spurs were concerned about some of Conte’s demands.
Their concerns included his reluctance to work with young players.
Conte led Inter to the Serie A title this season, but chose to leave after the club decided to implement big cuts and look to raise funds by selling players.
The serial winner was linked with the post at Real Madrid, but Carlo Ancelotti has been appointed.
It remains to be seen who Tottenham will turn to with their talks with Conte appearing to have now firmly reached a dead end.