The 27-year-old winger wants pay-back for the 8-0 defeat against Liverpool in 2007.
Olcay spoke with local reporters following the Europa League draw in Nyom.
“We are happy to have drawn Liverpool. The time has come for us to get revenge,” Olcay said.
“There is a score to settle following the 8-0 defeat.
“We want to make our fans happy and are aiming to win the Europa League.
“If we are to win the competition, we need to eliminate Liverpool.”
Beşiktaş have played Premier League opposition four times this season. The Black Eagles lost 1-0 to Arsenal over two legs in the Champions League playoffs.
The Turkish giants also drew against Tottenham in London and beat Spurs in Istanbul in the Europa League group stages
Olcay has six assists and has scrod five goals in 22 games this season.