The 21-year-old has seen his time at Anfield decimated after suffering successive cruciate ligament injuries, and now finds himself out on loan with Swiss club FC Luzern - who are coached by former Reds full-back Markus Babbel.
Despite being away from Melwood, and thus, unable to impress Klopp in training, Yesil is optimistic about his chances of breaking into the first-team upon his return.
When asked about whether he'd been in contact with Klopp, Yesil replied: "I prefer to speak with goals than to send him Christmas cards. We'll talk to each other when the time comes."
"I know my quality and trust myself, I'll push through there [Liverpool]. But for now it is about collecting match practice with Luzern," he added.
Yesil has made a slow start out on loan, with just one goal coming in his first eight games, and with the way his parent club are currently playing, it will be a very tough challenge for the German to make the grade on Merseyside.
Given the problems the Reds endured last season - where they attempted to replace Barcelona-bound Luis Suarez with Mario Balotelli, Rickie Lambert and Fabio Borini, and also had to deal with Daniel Sturridge spending large parts of the campaign out injured - the club seemed determined to ensure that the squad this time around was going to be capable of finding the back of the net.
While Divock Origi - who was another signing from the previous summer - arrived following a loan spell with Lille, the club also invested in Christian Benteke, Danny Ings and Roberto Firmino.
The trio have all shone at times this season, and while Ings and Benteke have spent time out injured, Firmino's performance against Manchester City indicated that Klopp's men have more than enough depth going forward, leaving Yesil's future up in the air.