Scottish left-back Tierney suffered ligament damage to his left knee in the 3-0 defeat at Liverpool on April 3 and was originally expected to miss between four and six weeks.
Such a timescale would have left Tierney facing the possibility of missing the remainder of the season, but Gunners boss Mikel Arteta provided a much more positive update ahead of Thursday's trip to Villarreal.
"He didn't need the surgery that we were afraid of," said Arteta.
"He's been working like a beast every single day. I don't know if he's going to make it tomorrow, but he certainly wants to be as close as possible."
Captain Aubameyang has not featured since April 8 and had been receiving treatment for malaria, but Arteta confirmed he and Lacazette (hamstring) are in line to feature.