The Frenchman has been in and out of the Arsenal team over the past season and a half.
The 29-year-old is out of contract in 2022, and may be moved on this month or in the summer if he does not sign a new deal.
And the Daily Mail reports Lacazette and manager Mikel Arteta are not on the best of terms.
If he does leave, Real and Atletico are the teams most likely to sign him.
Real have a need for a striker after letting Luka Jovic go to Eintracht Frankfurt on loan.
Atletico have a long standing interest in Lacazette.