The Italy international, who is co-owned by Juventus, has been heavily linked with a move to Signal Iduna Park after netting 22 goals in Serie A last season and the BVB boss has now admitted that the 24-year-old is one of his primary transfer targets.
"The forwards that I want cost more but they are also the best in circulation," Klopp is quoted as saying by Tuttosport. "We are willing to do everything to bring Immobile to us."
As for Immobile, he has insisted that he does not regret publicly expressing his desire to play Champions League football earlier in the week.
"I didn't want to blame anyway or to upset anyone, but I said what I felt in that moment," he explained.
"I have thanked the president [Urbano Cairo] and the fans, who have treated me as an important player.
"However, the ambitions I havea are those that stated in the press conference."
Immobile, who has been included in Italy's provisional World Cup squad, joined Torino from Genoa last year.