According to French outlet L’Équipe, both clubs are interested in luring the Arsenal forward away this summer, and have opened discussions over a possible deal.
Inter Milan have also reportedly sounded out the forward, as they plan for the possible departure of Lautaro Martinez.
Atletico Madrid have been heavily linked with the striker since his time at Lyon, but the striker would go on to join Arsenal in 2017.
However, Diego Simeone’s side remain keen on signing the France international, and reports claim the La Liga side could include Thomas Partey in any potential deal.
Like Atletico, Juventus could also offer a player in their attempts to sign Lacazette, and some Arsenal supporters have already taken to social media to declare that they would like to re-sign Aaron Ramsey.
The Welsh midfielder left Arsenal last summer on a free transfer, but has struggled for consistent gametime during his first season in Turin.
And some Arsenal fans believe a return to north London would be the ideal situation for both parties.
Some fans also tweeted tongue-in-cheek messages about signing Cristiano Ronaldo in exchange.
Arsenal boss Mikel Arteta has admitted that Arsenal are yet to open talks with Lacazette over a new contract at the Emirates, with his deal expiring in 2022.
But Arteta says the Gunners are in no rush to open negotiations with the striker, and says the club will commence talks when the time is right.
“We have to have a chat about the next step with him and get his idea, his feeling,” Arteta said during his pre-match press conference.
“As I said, I’m really happy with him. He’s a player I always liked, even when I wasn’t here because what he brings to the team, his qualities, his ability, his work rate so let’s see.
“Right now we are in a crucial moment, it’s not time to talk about a lot of contractual situations, we still have time and we will do it in the right moment.”