Lacazette had set his sights on a summer move to Atletico Madrid until a transfer ban until January for signing under age-players was upheld.
Reds boss Jurgen Klopp has set his sights on signing a big-name striker this summer and Lacazette certainly fits the bill.
He scored 37 goals in all competitions this season and has emerged at the top of Klopp’s wanted list of strikers.
Lyon have not given up hope that Lacazette will remain with them in Ligue 1 next season but he is determined to play in the Champions League.
Liverpool boss Jurgen Klopp wants to sign Alexandre Lacazette (right) Alexandre Lacazette odds: Who will sign Lyon star? Fri, June 2, 2017
Alexandre Lacazette has been linked with a big money move but who will sign the Lyon star?
Play slideshow Borussia Dortmund/Getty Images 1 of 7
Dortmund – 25/1
Liverpool could hold talks with Alexandre Lacazette's representatives this week
The Reds can offer him a chance to play in European football’s elite competition and the Sunday Express understands that Liverpool could meet his advisors next week.
Lacazette is one of the players that United boss Jose Mourinho is considering after ditching his interest in Antoine Griezmann who Lacazette was supposed to replace in Madrid.
But Liverpool are confident that Lacazette is far enough down Mourinho’s list that they won’t pose any problems when they look to complete the deal.
Lyon chairman Jean-Michel Aulas recently said the club will discuss with Lacazette regarding his future.
Get Quotes on Home Insurance
Jurgen Klopp has put Alexandre Lacazette at the top of his wanted list of strikers
“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.