Berardi is currently playing for Sassuolo in Serie A and could be one of the hottest properties on the market this summer.
AC Milan are reported to be weighing up a bid for the attacker, who scored eight goals Serie A last season and has five caps for the national team.
He would be open to the move but admits he would prefer to move to a team in the Champions League.
And the 24-year-old says Liverpool would be his first choice if he were to move on from his boyhood club after seven years.
“If an offer arrives, be it from Milan or another club, I will evaluate it with my club,” he said.
“And if I hear that it is the right proposal, to be taken on the fly, this time I will say to Sassuolo: ‘I’ll take it’.
“Being able to choose, I would play in Liverpool. Changing remains difficult for me, but it no longer frightens me, I would do it.
“The next goal is to play in Europe, but at a club where I can be used a lot, if not always. That is my priority.”
Liverpool are set to go into the market in the summer and signing a new forward will be a priority for Klopp.
They recently revealed that Daniel Sturridge is on the list of players who will be released in the summer and will need a replacement.
Lyon star Nail Fekir can play across the frontline or in midfield and is understood to be high on their list of targets.
Fekir was on the brink of a move to Anfield this time last year but complications with his medical meant the deal fell through.
It is anticipated Liverpool will go back in with another offer and Lyon president Jean-Michel Aulas recently revealed he expects his star player to leave.
“Thanks Nabil for bringing what he brought,” he said. “We have an understanding to let him go.”
Lyon are also facing a battle to keep hold of the lies of Tanguy Ndombele, Ferland Mendy, Moussa Dembele and Memphis Depay.
Former Manchester United attacked Depay has also been linked with Liverpool.
