He scored 37 goals in all competitions this season and has emerged at the top of Klopp's wanted list of strikers.
And Liverpool could meet his advisors this week.
Lyon chairman Jean-Michel Aulas recently said the club will discuss with Lacazette regarding his future.
“We will have to meet with Alex again," he said.
“We will have to see what will happen in the future, but today the decision to let Alexandre go is now under scrutiny.
“I would prefer that he stays. In the context of our competitiveness and our desire to build a truly great team for next season.
"Lyon has a lot of very good players and if Alexandre does not leave it will be another player in very similar conditions."