The left-back is reportedly having a medical with the Reds next week and signing as a back up for Andy Roberston.
The Reds moved for Tsimikas from Olympiacos after they could not agree a deal with Norwich City for Jamal Lewis.
The Premier League club wanted too much money, and the Reds are getting Tsimikas for £11.75 million.
Leicester had also been interested in the 24-year-old Greece international as a potential replacement for ben Chilwell.
He is expected to sign a four-year deal with Liverpool once his medical is completed.