The French club have told the forward he can either sign a new contract or leave the club and will not stand in his way if he wishes to move to the Premier League.
The 24-year-old has been heavily linked with a move to the Gunners or Liverpool this summer and it appears the Anfield club are now in prime position, ahead of Arsenal, to land the France international.
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These reports come from French newspaper L'Equipe who claim the players actions in recent weeks have led to a breakdown in the relationship between the club and Lacazette.
According to the publication, the Lyon forwards poor performance in the Trophee des Champions, his arrogant attitude and actions throughout the summer have lead to Lyon coach Hubert Fournier becoming angered with the striker.
The Red's have been put on high alert by the situation that is unravelling at Lyon, and are poised to step in should the player reject the offer of a new contract.
Lacazette scored 31 goals in 40 appearances during a prolific campaign for the French side, and Liverpool boss Brendan Rodgers could bring him in as he continues to revamp the Merseyside club's front line.
Rodgers has already added Christian Benteke, Danny Ings and Roberto Firmino this summer, along with Divock Origi returning from a loan spell at Lille.
With Mario Balotelli closing in a move to Lazio, given they qualify for the Champions League, and the sale of Rickie Lambert to West Brom. Liverpool are completely reshaping their attack. Fabio Borini is also surplus to requirements.
Arsenal have also been linked with Lacazette, who has scored 70 goals in 186 appearances for Lyon, however talk of a move to the Emirates has died down in recent weeks.
Theo Walcott was give the nod to start as the lone striker in the 1-0 win over Chelsea in the Community Shield final but failed to find the back of the net before being subbed for Olivier Giroud after 66 minutes.
It appears Arsene Wenger fancies Walcott through the middle, if the England international can keep himself free of injury, and he will be vying with Giroud, who scored 14 goals in 27 league games, for the solitary strikers spot.
Danny Welbeck is also capable of occupying the lone striker role but has only recently returned to training following a knee problem.
The North London club have been linked with with Karim Benzema, despite Wenger claiming it could not be further from the truth. While both Arsenal and Liverpool are set to do battle for Real Madrid winner Denis Cheryshev.
Liverpool and Arsenal fans: Would you like Alexandre Lacazette to sign for your club? Have your say below!