Both Dortmund's head coach and captain have believe the Italian striker has made a big impression since his arrival from Torino
Immobile signed for Dortmund from Torino for €18.5 million (£14.7m) in June after the 24-year-old scored 22 goals to become the top scorer in Serie A last season.
Despite a delayed start to pre-season after his inclusion in Italy's World Cup campaign - meaning he has only managed 45 minutes against Osnabruck so far - Klopp stated that Immobile has already made an impression at the club.
"He has hardly trained and has already shown his goalscoring ability," said Klopp to reporters.
Immobile, who was signed as a replacement for Robert Lewandowski after his free transfer to Bayer Munich, also received encouraging words from club captain Sebastien Kehl team-mate Oliver Kirch.
"We expect a lot from him. It has been seen that he is a true poacher, if he has the chance," said Kirch.
Kehl added: "It has been noted already in the first few days, that he is a really open, accessible type. In the training camp we will get to know him even better."
Immobile is expected to make his competitive debut for Dortmund in their Bundesliga opener against Bayer Leverkusen on August 23.