The Blues summer signing has struggled to hold down a regular starting spot in Frank Lampard’s team so far this season despite moving to the west London side in a £58m deal earlier this year.
Pulisic arrived at Chelsea FC with a big reputation following his stint as a key player in the Borussia Dortmund side to earn interest from a number of top European clubs.
The Blues won the race to sign Pulisic in January before the American playmaker linked up with his new team-mates in the summer.
However, Pulisic hasn’t played in four of Chelsea FC’s last five games despite Chelsea FC’s huge outlay on the attacking midfielder.
Former Spurs striker Klinsmann, who previously managed the United States team, has now offered some advice to Pulisic.
“You never know it’s the right fit unless you do it,” Klinsmann told ESPN.
“Christian did well to say: ‘I’m going to throw myself in another cold water, go over to London and throw myself in the Premier League, and I have to fight through the system there’. So that’s what he’s in.
“He’s a very special player, he’s tremendously talented, but this is a big step because Borussia Dortmund was also basically the club where he got formed into a professional player.
“He came out of the youth system there, he moved himself up, he had all the support within the club and now going to London – also to one of the biggest clubs in the world – you’ve got to bring your elbows out.”
He continued: “You don’t have that automatic assurance at Chelsea. At Chelsea it goes from game to game, week to week.
“You’re basically in training and you have to tell the coach: ‘I’m in, I’m going to start this game.’ So it’s a little bit more cold, it’s a bit more nasty.
“What I mean with the elbows is that you have to become nasty in order to make yourself a starter.”
Chelsea FC secured their first home Premier League win under new manager Lampard on Saturday thanks to a 2-0 victory over Brighton and Hove Albion.
Pulisic didn’t come off the bench during the west London side’s straightforward win at Stamford Bridge.
Chelsea FC will make the trip to Ligue 1 side Lille in the Champions League group stage on Wednesday night.
The Blues will then make the trip to Southampton in their next Premier League game.
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