The Reds are understood to have admired Chiesa for some time and they have recently revived their interest in the 25-year-old ahead of the new campaign.
Chiesa has been tipped to leave Juventus, who were deducted 10 points in Serie A last season following an investigating into the club's transfer dealings and finished in seventh place, subsequently failing to qualify for the Champions League.
The Italy international has been plagued with injuries over the last two seasons with Juve and he was reduced to just 11 starts across all tournaments in the 2022-23 campaign.
However, the winger's impressive efforts in his debut season with the Old Lady in 2020-21 - in which he recording 15 goals and 11 assists in 46 games before steering Italy to Euro 2020 glory - have seemingly not been forgotten as a number of top European clubs still hold an interest in the former Fiorentina man.
A recent report claims that Chiesa's agent Fali Ramadani travelled to England to hold talks regarding his client's future amid interest from Premier League quartet Liverpool, Chelsea, Arsenal and Newcastle United.
According to Gazzetta dello Sport, both Liverpool and Newcastle could accelerate their pursuit of Chiesa if a star name were to leave this summer.
In Liverpool's case, the report claims that a potential departure for Salah would be required if Jurgen Klopp's side were to push forward with a deal to sign Chiesa.
Newcastle, meanwhile, have both Chiesa and Leicester City's Harvey Barnes on their radar, but they may have to cash in on Allan Saint-Maximin to balance their books.
Since joining Liverpool from Roma in 2017, Salah has earned legendary status at Anfield having scored an impressive 186 goals and registered 79 assists in 305 appearances for the Reds across all competitions.
The 31-year-old has won seven trophies with the Merseysiders including the Premier League and Champions League and he is regarded as an integral first-team player for Klopp.
Salah, who has reportedly attracted interest from Saudi Arabia, still has three years remaining on his contract which he signed last summer, and the attacker is thought to have no immediate plans to leave the Reds.
Meanwhile, Chiesa also has three years left on his deal with Juventus, who will only entertain offers of at least €50m (£42.6m) for the winger.