The German, who had two separate spells with the north London club as a player, has enjoyed success with the USMNT but Spurs have been encouraged to look elsewhere.
The U.S. national team head coach has been linked with the White Hart Lane hot seat following Andre Villas-Boas' departure on Monday.
The former Germany striker, who has also been linked with the Switzerland job, was a big fan favorite during two spells at the north London club in his playing days and would be a popular appointment.
However, the 49-year-old signed a contract extension until 2018 last week after guiding the USA to next year's World Cup in Brazil and Gulati has no intention of allowing him to move on.
"We are not oblivious to the fact Jurgen's success has attracted interest from outside the U.S.," he told The Sun. "Therefore there were pragmatic market considerations in offering him a new long-term contract.
"It's not specifically the Switzerland or Tottenham issues - but the desire to have a commitment from him, contractually, for a long time is vital."
Klinsmann has taken the USA from 36th in the world - the team's lowest-ever FIFA ranking - to a current standing of 14th. The team also topped the final CONCACAF stage by four points to secure passage to Brazil.