The former Germany striker has been out of work since stepping down as manager of Hertha Berlin in February 2020.
Klinsmann earned cult hero status among the Tottenham Hotspur faithful during two spells as a player in North London back in the 1990’s.
Tottenham have been searching for a new manager ever since Jose Mourinho was sacked in April, with Ryan Mason brought in to hold the fort until the end of the season.
Former Chelsea and Inter Milan manager Antonio Conte was contacted for the role but an agreement could not be reached while an approach for Mauricio Pochettino was blocked by Paris Saint Germain.
In recent days, deals for Paulo Fonseca and Gennaro Gattuso have all fallen through.
Klinsmann, who has also managed the German national team, Bayern Munich and the U.S national team in the past, has revealed he has contacted Spurs chairman Daniel Levy about replacing Mourinho as manager.
“I called him after he let Mourinho go,” revealed Klinsmann while working as a pundit for the BBC on Friday.
“I said, ‘Daniel what is the case now?’. He said, ‘I have so much to do to sort things out at the club. Let’s talk a little later on’.
“Then I saw all the different names walking in, talking. . . and walking out. The same today.
“Spurs is in my heart. Would I be interested in the job? Absolutely. But if he [Levy] does not want to, I cannot force him.”