The 29-year-old is not agitating to leave but is believed to be seeking assurances on his role under manager Mikel Arteta next season, given the ongoing uncertainty over whether Pierre-Emerick Aubameyang will remain at the club.
Arsenal are privately adamant they will not lose both Aubameyang and Lacazette this summer, sources have told ESPN, and Arteta is ready to personally involve himself in talks to convince the Gabon striker to sign an extension to his contract, which expires in 2021.
Lacazette's deal runs out a year later, meaning that the club are in a stronger position to negotiate with the striker. However, Arteta has been told that player sales will be key to boosting funds to overhaul his squad in the transfer market this summer. The Frenchman could fetch as much as £60 million this summer.
That has led to speculation Lacazette may be made available if Aubameyang commits his future to Arsenal, with Atletico continuing to maintain an interest despite standing on the brink of completing the permanent signing of Alvaro Morata from Chelsea.
Arsenal could then pursue other targets with Atletico's Thomas Partey still of interest. Despite several stories suggesting a swap deal has been discussed, sources have told ESPN that the two clubs have not yet explored this option in any serious detail due to Arsenal's reluctance to make a definitive decision on Lacazette while Aubameyang's future is unclear.
Talks with both Aubemeyang and Lacazette have been delayed by the coronavirus pandemic, but the club know resolving the situation with their two star strikers is central to wider squad planning.
The pair are good friends but both want to hear the club's vision under Arteta, particularly in light of the financial pressures many Premier League clubs are experiencing as a result of the virus.
Arsenal remain the only English top-flight club to have negotiated a pay cut, rather than a wage deferral, with the vast majority of their first-team squad.
Midfielder Mesut Ozil is continuing to receive his full £350,000-a-week salary, but almost all other players agreed a 12.5% cut for 12 months from last April.
Arsenal face Manchester City on June 17 in their first Premier League match since play was suspended by the pandemic.