Garcia, who won the Champions League during his time at Anfield, thinks now is the time for Klopp to make Liverpool relevant again on the European stage.
Liverpool were thrashed 5-0 by Manchester City on Saturday but return to European action on Wednesday night as they welcome Sevilla to Anfield.
It will be the Reds' first Champions League game since 2015, when they went out at the group stages, while their last appearance in the knockout stages of the competition came back in 2009.
Garcia scored a 'ghost goal' in the 2005 semi-final against Chelsea which helped Liverpool on their way to an unforgettable comeback victory over AC Milan in the final, and the Spaniard is urging Klopp to make sure the club can enjoy similar occasions again.
"I think, for him, this has to be the season," said Garcia.
"He has been at the club almost two years. He has been trying to build a team similar to the one he had back in Germany and this has to be the season where the trophies are coming back to the club.
"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."
But are Jurgen Klopp's side capable of winning the Champions League?
"It depends," added Garcia. "If you look at the players and some of their performances, you can say why not?
"When I was here, no one in Europe really knew too much about us until we reached the final in 2005. Everyone was surprised, but I think the team now is a lot better than back then."