Both were out of contract this summer.
Can, who joined from Bundesliga side Bayer Leverkusen in 2014, looks set to join Juventus in Serie A.
The 24-year-old played his 167th and final game for Liverpool in last month's Champions League final defeat by Real Madrid and has not been included in champions Germany's World Cup squad.
Liverpool have already announced the signing of Brazilian midfielder Fabinho from AS Monaco for a fee that British media put at about 40 million pounds ($54 million).
Flanagan, 25, made headlines earlier this year when he was sentenced to a 12-month community order for assaulting his partner.
The Liverpool-born academy graduate made 51 senior appearances for the Merseyside club but his last game was a League Cup defeat to Leicester City in September 2017.
Capped once by England in a friendly international, he spent the end of last season on loan to Championship side Bolton Wanderers.
($1 = 0.7462 pounds)
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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