The Reds have made landing a left-back a priority this summer as they look to secure cover for Andrew Robertson.
They have had a bid for Norwich City's Jamal Lewis knocked back and are not prepared to meet his £20m asking price.
Instead Liverpool are set to pay £11m to take Olympiacos defender Tsimikas to Anfield this summer and their interest in the player has been long in the making.
He has been on Liverpool's radar for three years, with the club first spotting him when he was on loan at Dutch side Willem II.
Former Liverpool star Pedro Chirivella was at Willem II at the time and Liverpool took note of Tsimikas, interest they are now set to make good on.
The 24-year-old progressed from the youth ranks at Olympiacos into the senior side and made his debut for the Greek giants in 2015.
They sent him out on loan to Denmark with Esbjerg and then to Willem II in the Netherlands.
Tsimikas has been capped on three occasions by Greece.