The 30-year-old forward is in the final year of his contract at Arsenal and as things stand, will be available on a free transfer next summer.
There has been little talk of Arsenal offering him a new deal and there are suggestions clubs outside England are prepared to hold talks with the player over a pre-contract from January onwards.
The Frenchman has remained committed at Arsenal and has been a key performer for the club.
Lacazette wants a long-term contract but Arsenal are not interested in agreeing on such a deal.
The club do not want to be saddled with an ageing player on big wages and do not want to offer him a new long term contract.
However, Arsenal are open to agreeing on a short-term deal that could keep the forward at the club beyond next summer.
Lacazette has been playing well and Mikel Arteta is open to him staying at the club beyond the end of the season.
But Arsenal are not prepared to have too many years on the Frenchman’s potential new deal.