Gunners boss Arsene Wenger had a £29.3million offer for Lacazette turned down last week and could yet go back for the £42m-rated Frenchman.
But if the Arsenal boss decides not to make another offer, as Lyon president Jean-Michel Aulas has hinted, then a move for Icardi would be next up.
Wenger failed in his bid to lure Leicester’s Jamie Vardy to The Emirates earlier this summer and with Lyon offering Lacazette a new deal, he could be thwarted yet again.
Inter yesterday opened the door for a move for Icardi after their president Erick Thohir revealed he is willing to listen to offers for the forward, 23, if they match his £50m asking price.
The Indonesian businessman would like to keep Icardi, who has scored of 52 goals in all competitions, since signing from Sampdoria in 2013.
He said: “All of us and Inter are hoping that figure goes above 60million euros.
“Inter will be here for hundreds of years but it is made of individuals who change each year.
Icardi has been linked with a switch to Napoli following Higuain’s move to Juventus.
It is rumoured they offered £50.7m but Thohir said: “We are hoping to receive a better offer.
“Mauro is an important player for us and our captain. However, players come and go.”
Aulas confirmed Arsenal made an official offer of £29.3m for Lacazette but the French club immediately rejected it and said they will only talk if the bid is increased to £42m.
Wenger has revealed he is seeking a striker but admitted prices being quoted were ‘scary’.
Speaking after their 2-1 win over MLS All-Stars in San Jose he said: “At the moment I do not have too many attacking options.
“But you look at the cheques everybody signs and it is quite scary. “That is what the Premier League is about just now.”