Jurgen Klopp’s side signed left-back Tsimikas, 24, from Olympiacos on Monday as a deputy for Andy Robertson.
And they are also monitoring Tzavidas, a 16-year-old striker who plays for Panathinaikos.
Scouts from the Premier League champions have watched Tzavidas in action for both club and country.
Tzavidas was the top scorer for Panathinaikos’ under-17 side last season and is also attracting interest from Juventus and Spanish clubs.
Novasports states that Liverpool have contacted his agent to collect some information.
Liverpool staff were keen to find out how much Tzavidas would cost and what his contract situation is.
Tzavidas has not yet signed a professional contract, meaning he could freely move abroad with Panathinaikos only due training fees.