The Reds could be in the market for an understudy goalkeeper for Alisson and Southampton player McCarthy, 29, offers Premier League experience.
Former Liverpool boss Brendan Rodgers was an admirer of the Guildford-born custodian, who has been capped once by England in the second half of a 3-0 friendly win over USA in November 2018, but the ECHO understands his name has not been discussed by the current management team.
Tokoz, 23, is a defensive midfielder from Besiktas who can also operate at right-back.
He broke into the Turkish national team earlier this year and has also been linked with a potential move to Italian club Udinese among others but the ECHO understands he is not even on Liverpool's radar.