Italian media outlet Calcio Insider, as quoted by the Daily Mirror, is reporting that the Merseyside outfit are leading the race to sign the 23-year-old in the summer transfer window.
The same article states that Tolisso wants to leave Bundesliga champions Bayern Munich less than 12 months after the France international moving to Bayern Munich in a €41m deal last summer.
According to the same story, the Bayern star was a big admirer of former Liverpool FC captain Steven Gerrard to fuel his interest in a switch to the 18-time English champions this summer.
Tolisso netted 10 goals in 40 games in all competitions last season to make a decent start to his career at the Bundesliga champions.
However, the France star has scored six times and has made four assists in 17 starts and nine substitute appearances during the 2017-18 season.
Liverpool FC have already signed Guinea international Naby Keita this summer after the Reds agreed a £48m deal from Bundesliga side RB Leipzig in 2017.
The Reds have also signed Brazil international Fabinho in a £39m deal from Ligue 1 side AS Monaco earlier this summer.
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