Klinsmann will come up against the former Ajax midfielder on Wednesday when his USA side take on Eriksen's Denmark in a friendly.
And the ex-Germany coach and Tottenham striker feels Eriksen will likely want to take his career to the next level, though he hopes any move away from north London is not imminent.
"There’s no bigger club than Tottenham," he joked with reporters when asked if Eriksen could play for a bigger club in the future. "Every player chooses their own path and sees their own limit, and I’m sure he wants to see his own limits and where he can go one day.
"For me, Tottenham was a wonderful experience and I wouldn’t have wanted to miss a second of it. But I chose to leave the club for Bayern Munich to win trophies.
"I hope he stays for a long time at Spurs. It’s a very competitive squad so theres no time for him to relax as someone will jump in and take his spot. I’m curious to see him for many more years at Tottenham."
He added: "He is an exceptional talent and that’s why he’s at Tottenham. He’s tremendously talented and seeing some of his goals this season and how he has been the difference in some of the games shows that he can turn it on.
"You always have to be very attentive and sharp on him. Having these types of players in your team gives you a spark."