Since the German's arrival in October 2015, Liverpool have reached the finals of both the EFL Cup and Europa League before losing out to Manchester City and Sevilla respectively.
Klopp has also earned the Merseyside giants a return to the Champions League, but Garcia has suggested that the German requires a trophy for his time at Anfield to be regarded as a success.
The 39-year-old is quoted by The Sun as saying: "He has been at the club almost two years. I think he is doing a good job.
"He has brought in some of the players he wanted, now is the time for him to show the team is ready to face everything."
Liverpool last won a competition when they emerged victorious in the 2011-12 EFL Cup, where they overcame Cardiff City on penalties in the final.