The 18-year-old, who is a Germany-born frontman of Turkish descent, is expected to undergo a medical today and will cost in the region of £1million.
Yesil, who had also attracted interest from Arsenal, shone in last year's Under-17 World Cup when he scored six goals in seven matches for Germany.
He has progressed through the youth ranks at Leverkusen and has been a prolific scorer for their under-19s.
Yesil is unlikely to go straight into Liverpool's first team squad as he's viewed as one for the future.