The Merseyside giants signed the Greek defender last year in their bid to bring in one more left-back as cover for Andrew Robertson.
However, the 25-year-old made just seven appearances last season and only two of them came in the Premier League, which amounted to just six minutes of league football.
Tsimikas could be open to a move away from the Reds as he wants to play more football and Napoli are interested in signing him.
The Serie A giants made a loan enquiry with Liverpool for the left-back, but according to Italian broadcaster RAI Sport’s Ciro Venerato, the answer from the Reds was in the negative.
Liverpool made it clear to Napoli that they are not interested in loaning out Tsimikas this summer.
The defender has been part of Liverpool’s pre-season preparation and Jurgen Klopp wants him to be part of his squad.
Tsimikas will hope that he plays more than six minutes of Premier League next season if he continues at Liverpool.