Speaking of Lacazette's possible departure, Genesio said "he can leave if Lyon want him to. There are some offers that you cannot refuse."
But Genesio added that if he had his way Lacazette would stay, and that he had the backing of higher-ups:
"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."
Arsenal already made a £30 million ($40 million) bid for the 25-year-old striker last week, which was turned down. But the club is expected to make an even more generous offer soon, as manager Arsene Wenger wants to strengthen the team's goal scoring capabilities - and Lyon could find the amount of money in play too hard to resist.
It would likelu be money well spent for the Gunners if Lacazette continues his current form. He has scored 92 goals in 230 appearances for Lyon, and has been on France's national team since 2013, though he has only made 10 appearences in that period.
Arsenal is ramping up its transfer activity after a fairly quiet summer so far. It's only major inward transfer has been Borussia Monchengladbach's Granit Xhaka for £34 million. But as well as Lacazette there are also rumours the club is after Valencia's Shkodran Mustafi - as long as it can get him for less than the £42 million price tag stipulated in his release clause.
Either way, Wenger does not have long to make any further signings if he wants new players to appear in the club's first Premier League game of the season - at home to Liverpool on August 14.