Lacazette, 28, has missed the last seven games in all competitions with an ankle problem.
Lacazette made an impressive start to the 2019/20 campaign with two goals in his first three appearances.
The Gunners predicted he would return to action this month and Tierney has shared an update to his Instagram page.
Tierney posted a picture of himself alongside the Frenchman on the training pitches at London Colney.
Alongside a laughing emoji, the former Celtic star wrote: "Wagwan @lacazettealex."