Lacazette, who only recently signed a new four-year deal at the Parc Olympique Lyonnais, was the subject of a failed £29.3m (€35million) bid from the Gunners last week.
And with Arsene Wenger hinting they’re ready to make an improved bid, the Gunners appear to have been handed encouragement in their pursuit of the France international striker.
“He can leave if Lyon want him to,” said the French club’s manager Bruno Genesio.
“There are some offers that you cannot refuse. My desire as manager is that the best players stay and Lacazette is very important for the team.
“I have been assured by my president that we will keep the player. You never know what could happen right up until August 31.”
Lyon president Jean-Michel Aulas has so far insisted the striker is not for sale at any price.
However, the French club are thought to value Lacazette at £40m and could be open to an offer from Arsenal if they are willing to meet this valuation.
Gunners boss Arsene Wenger is keen to add to his squad ahead of the new Premier League season after already securing the signings of Granit Xhaka, Takuma Asano and Rob Holding.
The Gunners are also keen on a move for Inter Milan forward Mauro Icardi and met with the Argentine’s agents on Monday.