The Brazilian shot-stopper is currently sidelined with a calf injury he picked up on the opening weekend of the Premier League season.
Former West Ham custodian Adrian is deputising for Alisson, with veteran Englishman Andy Lonergan serving as third-choice goalkeeper.
However, with Adrian set to turn 33 in January, the Reds want to secure a more long-term No.2
Liverpool scouts watched the 23-year-old Cakir in action against Fenerbahce at the weekend and were impressed by what they saw.
The Turkey international is valued at around £14m and could be the subject of a bid from Liverpool in January or next summer.
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